Microwave acceleration of carbon gasification reactions

ABSTRACT

A method for the gasification of carbon to yield products including carbon monoxide, hydrogen, and methane. The method comprises irradiating a source of carbon with radiation having a frequency between 300 GHz and 300 MHz and contacting the source of carbon with a reactant such as water, carbon dioxide, hydrogen, and a nitrogen oxide. The choice of reactant dictates the resultant product.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application claims priority from U.S. Provisional Application Ser. No. 62/001,910 filed May 22, 2014, the disclosure of which is incorporated herein as if set forth in its entirety.

FIELD OF THE INVENTION

The present invention generally relates to a method for the gasification of carbon materials, and more specifically a method for accelerating the gasification of carbon materials by irradiation with microwave radiation.

BACKGROUND OF THE INVENTION

The remediation of carbon dioxide emitted into the atmosphere, primarily from energy-generation combustion processes, is of considerable concern due to the profound contribution it makes to the processes of global warming. See Mann, M. E.; Bradley, R. S.; Hughes, M. K. Global-scale Temperature Patterns and Climate Forcing over the Past Six Centuries Nature 1998, 392, 779-787. Although there a number of proposed remediation schemes, including geoengineering (sequestration) and rapid carbonate formation, among the most appealing is the reduction of CO₂ to more synthetically useful molecules. See Schellnhuber, H. J. Geoengineering: The Good, the MAD, and the Sensible Proceedings of the National Academy of Sciences 2011, 108, 20277-20278; Hileman, B. GlobalL Climate Change Chemical & Engineering News Archive 1997, 75, 8-16; Lim, M.; Han, G.-C.; Ahn, J.-W.; You, K.-S. Environmental Remediation and Conversion of Carbon Dioxide (CO₂) into Useful Green Products by Accelerated Carbonation Technology Int. J. of En. Res. and Pub. Health 2010, 7, 203-228; Kriegler, E.; Edenhofer, O.; Reuster, L.; Luderer, G.; Klein, D. I Atmospheric Carbon Dioxide Removal a Game Changer for Climate Change Mitigation? Clim. Change 2013, 118, 45-57; Yin, X.; Moss, J. R. Recent developments in the activation of carbon dioxide by metal complexes Coord. Chem. Rev. 999, 181, 27-59; and Edwards, J. H. Potential Sources of CO₂ and the Options for Its Large-Scale Utilization Now and in the Future Catal. Today 1995, 23, 59-66. Unfortunately, this is extremely difficult to accomplish due to the high thermodynamic stability of CO₂.

The following reaction is among the oldest and simplest methods to activate CO₂ is its reaction with carbon to produce carbon monoxide:

C+CO₂⇄2CO ΔH=172 kJ/mole

This reaction, called the Boudouard reaction after its discoverer, has been known since 1905 and is one of the equilibria that occur during the gasification of coal and other carbon-rich sources. See Walker Jr, P. L.; Rusinko Jr, F.; Austin, L. G. Gas Reactions of Carbon. In Advan. in Cat.; D. D. Eley, P. W. S., Paul, B. W., Eds.; Academic Press, 1959; Vol. Volume 11; pp 133-221. The Boudouard reaction represents a simple and straightforward method for the remediation of carbon dioxide in the environment through reduction.

The reaction is highly endothermic; as such, the equilibrium lies far to the left, with CO₂ being the favored product. Accordingly, due to the large positive enthalpy, typically reported to be 172 kJ/mole under standard conditions at 298 K, the equilibrium does not favor CO production until temperatures>700° C., when the entropic term, −TΔS, begins to dominate and the free energy becomes negative. The free energy of the formation of CO₂ is relatively insensitive to temperature while the entropy is positive; at high temperatures (>700° C. is typically cited), the free energy change becomes negative, making CO formation progressively more favored. See Reed, T. B. Free Energy of Formation of Binary Compounds: an Atlas of Charts for High-Temperature Chemical Calculations; MIT Press: Cambridge, Mass., 1971. For this reason, the reaction only plays a significant role in high-temperature (>900° C.) gasification and smelting processes. See Walker Jr, P. L.; Rusinko Jr, F.; Austin, L. G. Gas Reactions of Carbon. In Advan. in Cat.; D. D. Eley, P. W. S., Paul, B. W., Eds.; Academic Press, 1959; Vol. Volume 11; pp 133-221; and Van Deventer, J. S. J.; Visser, P. R. On the Role of the Boudouard Reaction in the Isothermal Reduction of Iron Ore by Char and Graphite Thermochim. Acta 1987, 111, 89-102.

The contemporary appeal of this reaction is that it potentially represents a means of CO₂ remediation by converting it to more synthetically flexible CO. Its use has been proposed as part of “clean coal” schemes that convert the CO₂ product gas to CO, which can then be used to produce hydrogen via the water-gas shift reaction or hydrocarbons through the Fischer-Trøpsch process. See Ratnasamy, C.; Wagner, J. P. Water Gas Shift Catalysis Catal. Rev. 2009, 51, 325-440; and Dry, M. E. The Fischer Tropsch Process: 1950-2000 Catalysis. Today 2002, 71, 227-241. In addition, there is a substantive synthetic chemistry whereby CO is utilized as a carbonylation reagent. See Beller, M.; Cornils, B.; Frohning, C. D.; Kohlpaintner, C. W. Progress in Hydroformylation and Carbonylation J. Mol. Cat. A, 1995, 104, 17-85. In short, while this reaction offers great potential for use in CO₂ remediation and utilization schemes, the high temperatures at which it occurs efficiently tend to preclude many of these.

The reaction between superheated steam and carbon to produce synthesis gas (See reaction 1 in the below equilibrium series) is part of the general category of gasification reactions used to obtain hydrogen from coal and other carbon-rich sources. See Higman, C.; van der Burgt, M. Gasification, 2nd ed.; Elsevier: Amsterdam, 2008; and Walker Jr., P. L.; Rusinko Jr, F.; Austin, L. G. Gas Reactions of Carbon. In Advances in Catalysis; D. D. Eley, P. W. S., Paul, B. W., Eds.; Academic Press: New York, 1959; Vol. 11; pp 133-221. Gasification reactions typically occur at temperatures≧700° C. depending on the carbon source, while industrial processes, such as coal gasification, run at much higher temperatures (>1000° C.). These high temperatures are required to drive the endothermic components of the primary reactions and to obtain useful reaction velocities. See Walker Jr., P. L.; Rusinko Jr, F.; Austin, L. G. Gas Reactions of Carbon. In Advances in Catalysis; D. D. Eley, P. W. S., Paul, B. W., Eds.; Academic Press: New York, 1959; Vol. 11; pp 133-221.

C+H₂O⇄CO+H₂ ΔH=+131 kJ/mol   (1)

CO+H₂O⇄CO₂+H₂ ΔH=−41 kJ/mol   (2)

C+CO₂⇄2CO ΔH=+172 kJ/mol   (3)

C+2H₂⇄CH₄ ΔH=−75 kJ/mol   (4)

Along with production of synthesis gas (rxn. 1), the reactions between carbon and high-temperature steam consist of a complex set of equilibria, which produce not only hydrogen and carbon monoxide but also carbon dioxide through the water-gas shift (WGS) reaction (rxn. 2), carbon monoxide through the disproportionation of carbon and carbon dioxide (Boudouard reaction, rxn. 3), and methane through the reaction of carbon and hydrogen (rxn. 4). The complexity of the equilibria, along with the primary steam-carbon reaction (rxn. 1) being very endothermic, means that the composition of the gases produced in gasification will depend critically on the temperature and pressure of the reaction.

Because of the industrial importance of these reactions in the production of hydrogen for direct use as a clean alternative fuel or for the production of hydrocarbons through the Fischer-Tropsch process, the development of less energy-intensive methods for driving these reactions is desirable. See Dry, M. E. The Fischer-Tropse Process: 1950-2000, Catalysis Today 2002, 71, 227-241; and Navarro, R. M.; Pena, M. A.; Fierro, J. L. G. Hydrogen Production Reactions from Carbon Feedstocks: Fossil Fuels and Biomass. Chem. Rev. 2007, 107, 3952-3991.

SUMMARY OF THE INVENTION

Accordingly, among the provisions of the present invention may be noted a method of gasifying a source of carbon. The method comprises irradiating the source of carbon with radiation having a frequency between 300 GHz and 300 MHz; and contacting the source of carbon with a reactant selected from the group consisting of water, carbon dioxide, hydrogen, nitrogen oxides having formula NO_(x) wherein x has a value between 0.5 and 2.5 (e.g., N₂O, NO, NO₂, etc.), and any combination thereof. The contact between the irradiated source of carbon and the reactant causes a reaction that yields a product selected from the group consisting of carbon monoxide, carbon dioxide, hydrogen, methane, nitrous oxide, nitric oxide, nitrogen, and any combination thereof.

In some embodiments, the frequency of radiation is between about 1 GHz and about 18 GHz, between about 1 GHz and about 6 GHz, between about 1.5 GHz and about 3 GHz, between about 3 GHz and about 6 GHz, between about 6 GHz and about 10 GHz, or between about 14 GHz and about 17 GHz.

In some embodiments, the microwave acts as the enabling technology, and the source of carbon and the reactant are also convectively heated.

In some embodiments, the source of carbon is selected from the group consisting of amorphous carbon, charcoal, activated charcoal, carbon black, coal, graphite, coke, carbonized biomass, fullerene, carbon nanotubes, polyaromatic hydrocarbons, and any combination thereof.

In some embodiments, the reactant comprises carbon dioxide, and the method yields a product comprising carbon monoxide.

In some embodiments, the reactant comprises water, and the method yields a product comprising carbon monoxide and hydrogen.

In some embodiments, the reactant comprises water, and the method yields a product comprising carbon monoxide, carbon dioxide, hydrogen, and methane.

In some embodiments, the reactant comprises steam, and the method yields a product comprising carbon monoxide and hydrogen.

In some embodiments, the reactant comprises steam, and the method yields a product comprising carbon monoxide, carbon dioxide, hydrogen, and methane.

In some embodiments, the reactant comprises hydrogen, and the method yields a product comprising methane.

In some embodiments, the microwave source will enable underground coal gasification.

Other objects and features will be in part apparent and in part pointed out hereinafter.

BRIEF DESCRIPTION OF THE DRAWING(S)

FIG. 1 is a schematic of apparatus used to measure kinetic data under microwave conditions.

FIG. 2 is a schematic of the flow system used to collect kinetic data under conventional thermal reaction conditions.

FIG. 3 is a schematic of closed cell used to acquire equilibrium data under microwave conditions.

FIG. 4 are graphs of the product gases evolved over time from the activated carbon in a flowing N₂ stream at 75, 100, 125 and 150 Watts of applied microwave power. The gases are H₂ (solid line -), CO (dashed line - -), and CO₂ (dashed line with dots -•-).

FIGS. 5A and 5B are graphs depicting the production of CO from the reaction of CO₂ with carbon as a function of time under (FIG. 5A) microwave and (FIG. 5B) thermal conditions.

FIG. 6 is an Arrhenius plot of the rate of CO evolution for the thermal and microwave-driven Boudouard reaction.

FIG. 7A shows the production of CO and CO₂ over time as a function of carbon temperature for the microwave (left) and thermal (right) reactions.

FIG. 7B shows CO and CO₂ as a percent of the total composition under steady-state conditions for the microwave (left) and thermal (right) reactions.

FIG. 8 shows the equilibrium constants as a function of temperature for microwave and thermal Boudouard reactions (trend lines are to guide the eye).

FIG. 9 shows the mole fraction of CO and CO₂ as a function of temperature for the microwave (solid line -) Boudouard reaction and thermal (dashed line - -) Boudouard reaction, predicted from the calculated equilibrium constants and assuming one atmosphere of pressure.

FIG. 10 depicts the proposed mechanism of the microwave-specific effect on the Boudouard reactions.

FIG. 11 depicts the equilibrium composition of gases (CH₄, CO₂, H₂O, CO, and H₂) as a percent of the total gas and as a function of temperature under microwave irradiation.

FIG. 12 depicts equilibrium constants as a function of temperature for microwave and thermal steam-carbon reactions.

FIG. 13 depicts equilibrium constants as a function of temperature for microwave and thermal Boudouard reactions.

FIG. 14 depicts equilibrium composition of the reactants and products of the steam-carbon reaction as a function of temperature under microwave (thin lines) and thermal (thick lines) conditions. The reactant is H₂O (solid line -). The products are H₂ (dashed line - -) and CO (dashed line with dots -•-). The vertical lines (perpendicular to the x-axis) represent microwave thresholds for product formation. The first vertical line represents the lowest temperature (power) at which any H₂ is observed, and the second vertical line represents the lowest temperature (power) at which equilibrium could be readily established in 100 minutes.

DETAILED DESCRIPTION OF THE EMBODIMENT(S) OF THE INVENTION

Recently, in the carbon-carbon dioxide (Boudouard) reaction (rxn. 3), the use of microwave radiation to heat the carbon results in a dramatic change in the observed thermodynamics of the reaction. See Hunt, J.; Ferrari, A.; Lita, A.; Crosswhite, M.; Ashley, B.; Stiegman, A. E. Microwave-Specific Enhancement of the Carbon-Carbon Dioxide (Boudouard) Reaction. J. Phys. Chem. C 2013, 117, 26871-26880. These thermodynamic changes result in an increase in the equilibrium constant so that carbon monoxide becomes the favored product at 213° C., compared to 643° C. when using conventional convective heating. These temperature values are calculated from the thermodynamic values. In practice, one may employ higher temperatures to ensure the reaction proceeds toward the desired product. Accordingly, the microwave may be used at 800° C., while a thermal reaction may need to use temperatures around 1000° C. to achieve the product. This is a rather profound effect that potentially allows the remediation of CO₂ to be carried out using the Boudouard reaction at temperatures well below what is possible using conventional heating. Given the importance of the general class of gas-carbon reactions in the overall scenario of energy production, it is useful to determine whether the thermodynamic benefits that microwave heating imparts to the Boudouard reaction are general for the other processes—in particular, the endothermic steam-carbon reaction.

We have found that under microwave irradiation to selectively heat carbon, dramatically different thermodynamics for the reaction are observed. During kinetic studies of the reaction under conditions of flowing CO₂, the apparent activation energy dropped from 118.4 kJ/mole under conventional convective heating to 38.5 kJ/mole under microwave irradiation. From measurement of the equilibrium constants as a function of temperature, the enthalpy of the reaction dropped from 183.3 kJ/mol at ˜1100 K to 33.4 kJ/mole at the same temperature under microwave irradiation. This changes the position of the equilibrium so that the temperature at which CO becomes the major product drops from 643° C. in the conventional thermal reaction to 213° C. in the microwave. The observed reduction in the apparent enthalpy of the microwave driven reaction, compared to what is determined for the thermal reaction from standard heats of formation, can be thought of as arising from additional energy being put into the carbon by the microwaves, effectively increasing its apparent standard enthalpy. Mechanistically, it is hypothesized that the enhanced reactivity arises from the interaction of CO₂ with the steady-state concentration of electron-hole pairs that are present at the surface of the carbon due to the space-charge mechanism, by which microwaves are known to heat carbon. Such a mechanism is unique to microwave-induced heating and, given the effect it has on the thermodynamics of the Boudouard reaction, suggests that its use may yield energy savings in driving the general class of gas-carbon reactions.

The steam-carbon reaction, which is the essential reaction of the gasification processes of carbon-based feed stocks (e.g., coal and biomass), produces synthesis gas (H₂+CO), a synthetically flexible, environmentally benign energy source. The reaction is very endothermic which mandates high temperatures and a large expenditure of energy to drive the reaction. We have found that using microwave irradiation to selectively heat the carbon leads to dramatically different observed thermodynamics for the reaction. From measurement of the equilibrium constants as a function of temperature, the enthalpy of the reaction under microwave radiation was found to become significantly more exothermic, dropping from 144.2 kJ/mol at the median reaction temperature of 880 K to 15.2 kJ/mol under microwave irradiation. The reaction conditions under which the steam-carbon reaction was run, and under which the equilibrium measurements were determined, consisted of three other reactions that came to equilibrium. These reactions were the Boudouard reaction, which is the reaction of CO₂ with carbon to form CO; the water-gas shift reaction, where CO and water react to form H₂ and CO₂; and the carbon-hydrogen reaction, which generates methane from the reaction of H₂ with carbon. We determined the equilibrium constants and thermodynamic parameters for all of these reactions. The Boudouard reaction, which is also strongly endothermic, was found to be more exothermic under microwave radiation (180.2 kJ/mol (thermal) and 27.0 kJ/mol (MW)). The water-gas shift reaction became more endothermic (−36.0 kJ/mol (thermal) and −11.4 kJ/mol (MW)). The carbon-hydrogen reaction also underwent an endothermic shift, from −79.7 kJ/mol to −9.1 kJ/mol. From the associated equilibrium expressions and the equilibrium constants for the steam-carbon reaction system, the mole fractions of the system components under thermal and microwave conditions were estimated. The effect of the microwave radiation was to change the position of the equilibrium so that the temperature at which H₂ was at a maximum dropped from 643° C. in the conventional thermal reaction to 213° C. in the microwave. Notwithstanding the predicted temperature shift, there was an observable threshold below which microwaves could not produce products. In our system, the minimum energy at which H₂ appeared was 373° C. (30 W), while the temperature at which equilibrium could be established in a reasonable period of time (100 min) was 491° C. (100 W).

The present invention is therefore directed to a method for accelerating and/or catalyzing carbon gasification reactions by microwave irradiation of a source of carbon. In some embodiments, the source of carbon is contacted with a reactant during microwave irradiation. The reactant may be selected from among water, carbon dioxide, hydrogen, nitrogen oxides having formula NO_(x) wherein x has a value between 0.5 and 2.5 (e.g., N₂O, NO, NO₂, etc.), and any combination thereof. In some embodiments, the present invention is directed to the use of microwave radiation to drive the Boudouard reaction, to thereby result in a dramatic change in the observed thermodynamics of the reaction, which pushes the equilibrium to the right, favoring the production of CO, at temperatures that are over 400° C. lower than can be achieved by conventional convective heating. It is currently believed that a change in the apparent thermodynamics of a reaction is due to the presence of microwave irradiation. This work opens up the possibility that through the use of microwaves, reactions that are thermodynamically unfavorable can be exploited at reasonable temperatures.

Additionally, the present invention is further directed to a method of accelerating the steam-carbon reaction by microwave irradiation of a source of carbon. The effect of microwave radiation on the observed thermodynamics of the steam-carbon reaction and the other equilibria that take place during the gasification process.

The present invention is predicated upon the discovery of a fundamental property of microwave driven reactions with carbon that no one had previously realized. This property is that, under microwave irradiation, the observed thermodynamics of the reactions disclosed herein change such that the reactions become much more thermodynamically favorable.

In some embodiments, the present invention is directed to a method of gasifying a source of carbon. The method comprises irradiating the source of carbon with radiation having a frequency between 300 GHz and 300 MHz. The frequencies recited herein encompass microwave radiation, and the frequencies correspond to radiation having wavelengths ranging from about 1 mm to about 1 meter. As is known, wavelength and frequency are related by the equation: f*λ=c, wherein f is the frequency in Hertz (Hz=1/second), λ is the wavelength (in meters), and c is the speed of light (299792458 meters/second).

The source of microwave may be selected from any commercial, industrial, or laboratory microwave system. In some embodiments, the oven may be run under conditions of fixed applied microwave power. To acquire flow (kinetic) and static (equilibrium) data, two reaction systems were designed and built to fit in the microwave cavity.

In some embodiments, the source of carbon is reacted with a reactant selected from among water, carbon dioxide, hydrogen, nitrogen oxides having formula NO_(x) wherein x has a value between 0.5 and 2.5 (e.g., N₂O, NO, NO₂, etc.), and any combination thereof. Preferably, the reactant comprises a reactant gas that is flowed over the source of carbon. In the flow system, the reactant gas passes up through the catalyst, which is positioned at the center of the microwave cavity. The reactant gas is introduced into the system using a calibrated mass-flow controller. The volume of the product gas stream as a function of time is then determined with a totalizing mass flow meter.

The static system for determining equilibrium constant is a closed reactant system that allows the reactant introduction of the gas into an evacuated cell and imitation of microwave irradiation of the same. The static system is suitable for determining equilibrium constants of the reactions; the flow system is expected to be more suitable for a commercialized process.

In both systems, the internal pressure is constantly measured using a transducer, and the temperature of the catalyst surface is measured in-situ using an external pyrometer that is focused on the surface through a germanium window. Both systems have a septum port that allows aliquots to be extracted and analyzed by gas chromatography. Details of the apparatus are provided below.

The frequency of radiation may be determined in part upon the spectral and dielectric properties of the source of carbon. Sources of carbon may vary in terms of the optimal frequency for excitation and heating. In some embodiments, the frequency of radiation is between about 1 GHz and about 18 GHz, between about 1 GHz and about 6 GHz, between about 1.5 GHz and about 3 GHz, between about 3 GHz and about 6 GHz, between about 6 GHz and about 10 GHz, or between about 14 GHz and about 17 GHz.

Any of a wide variety of laboratory grade or even commercial grade microwave ovens capable of providing sufficient power to heat the source of carbon are suitable for use in the present invention. Consumer ovens usually use 2.45 gigahertz (GHz), which corresponds to wavelength of 12.2 centimeters (4.80 in). Large industrial/commercial ovens often use 915 megahertz (MHz), which corresponds to wavelength of 32.8 centimeters (12.9 in). In some embodiments, the power of the microwave radiation may be up to about 1500 W, or up to about 1000 W, such as between about 75 W and about 1500 W, or between about 75 W and about 1000 W, or between about 75 W and about 500 W, or between about 75 W and about 200 W. In some preferred embodiments, the microwave power may be at least about 200 W, such as about 300 W.

The carbon source may comprise any carbon capable of absorbing microwave radiation. In some embodiments, the carbon source may be any solid carbon capable of absorbing microwave radiation. Suitable sources of carbon for the method of the present invention include any source of carbon capable of absorbing microwave radiation and heating thereby. Suitable sources of carbon include amorphous carbon, charcoal, activated charcoal, carbon black, coal, graphite, coke, carbonized biomass, fullerene, carbon nanotubes, polyaromatic hydrocarbons, and any combination thereof.

In some embodiments, the carbon source comprises steam activated charcoal. Commercially available steam activated charcoal (50-200 mesh) with a surface area of 992.3 m²/g may be obtained from Fisher and used as received.

In some embodiments, the carbon source comprises graphite (Fisher, Grade #38). Graphite may be obtained as granular powder, with observable particle sizes between ˜6 to 60 μm, and a BET surface area of 7.6 m²/g for the material.

According to the method of the present invention, the microwave-irradiated source of carbon is contacted with a reactant selected from the group consisting of water, carbon dioxide, hydrogen, and any combination thereof. The reactant is typically contacted with the source of carbon in a gaseous form. For example, water is brought into contact with the source of carbon as steam. The volume of gas introduced may be a fixed amount, determined in part upon the total mass of the source of carbon. Alternatively, the volume of gas may be provided by continuously flowing the gas over the source of carbon.

Microwave radiation is suitable to accelerate or catalyze an array of carbon gasification reactions, as set forth in the following reactions (1)-(4):

C+H₂O⇄CO+H₂ ΔH=+131 kJ/mol   (1)

CO+H₂O⇄CO₂+H₂ ΔH=−41 kJ/mol   (2)

C+CO₂⇄2CO ΔH=+172 kJ/mol   (3)

C+2H₂⇄CH₄ ΔH=−75 kJ/mol   (4)

As shown in the reactions (1)-(4), the contact between the microwave-irradiated source of carbon and the reactant causes a reaction that may yield one or more of several products, including carbon monoxide, carbon dioxide, hydrogen, methane, and any possible combination thereof.

In some embodiments, the microwave acts as the enabling technology, and the source of carbon and the reactant are also convectively heated. In this capacity the microwave source could be integrated into a larger convectively heated gasification processes system to reduce average energy costs. The microwave source will facilitate non-traditional gasification technology such as in-ground coal gasification.

In some embodiments, the method of the present invention accelerates the Boudouard reaction. Accordingly, the microwave-irradiated source of carbon may be contacted with carbon dioxide. Carbon dioxide (99.9999% purity) may be obtained from Airgas and used as received. The source of carbon that is heated by microwave irradiation reacts with the carbon dioxide to thereby yield 2 moles carbon monoxide for every mole or carbon and every mole of carbon dioxide. The carbon dioxide may be continuously flowed over the microwave-irradiated source of carbon, or the reaction may occur under batch conditions. In some embodiments, the applied microwave power for this reaction may vary between about 50 W and about 2000 W, between about 75 W and about 1500 W, or between about 75 W and about 1000 W, or between about 75 W and about 500 W, or between about 75 W and about 200 W. In some embodiments, the temperature of the reaction may be between about 600° C. and about 1200° C., such as between about 800° C. and about 1000° C. In some embodiments, the microwave frequency is 2.45 GHz, which is suitable since commercial microwaves operate due to regulations.

Accordingly, in some embodiments, the method of the present invention enables gasification of a microwave irradiate source of carbon by contact with carbon dioxide at a temperature less than 1000° C. in which the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 1:1, at least about 3:2, at least about 2:1, at least about 5:2, or even at least about 3:1. In some embodiments, the method of the present invention enables gasification of a microwave irradiate source of carbon by contact with carbon dioxide at a temperature less than 920° C. in which the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 1:1, at least about 3:2, at least about 2:1, at least about 5:2, or even at least about 3:1. In some embodiments, the method of the present invention enables gasification of a microwave irradiate source of carbon by contact with carbon dioxide at a temperature less than 850° C. in which the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 1:1, at least about 3:2, at least about 2:1, at least about 5:2, or even at least about 3:1. In some embodiments, the method of the present invention enables gasification of a microwave irradiate source of carbon by contact with carbon dioxide at a temperature less than 820° C. in which the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 1:1, at least about 3:2, at least about 2:1, at least about 5:2, or even at least about 3:1.

In some embodiments, the method of the present invention accelerates the formation of synthetic gas. Accordingly, the microwave-irradiated source of carbon may be contacted with water. Typically, the source of carbon is contacted with steam. The steam may be continuously flowed over the microwave-irradiated source of carbon, or the reaction may occur under batch conditions. The source of carbon that is heated by microwave irradiation reacts with the water to thereby yield one mole carbon monoxide and one mole hydrogen for every mole or carbon and every mole of water. The product carbon monoxide and hydrogen may further react with each other or with carbon to yield a variety of products, as shown in reactions (2), (3), and (4). Accordingly, the method of the present invention encompasses further reaction in which the products include carbon monoxide, carbon dioxide, hydrogen, and methane. In some embodiments, the applied microwave power for this reaction may vary between about 50 W and about 2000 W, between about 75 W and about 1500 W, or between about 75 W and about 1000 W, or between about 75 W and about 500 W, or between about 75 W and about 200 W. In some embodiments, the temperature of the reaction may be between about 600° C. and about 1200° C., such as between about 800° C. and about 1000° C.

In some embodiments, the method of the present invention accelerates reaction between a source of carbon and hydrogen. Accordingly, the microwave-irradiated source of carbon may be contacted with hydrogen. The hydrogen may be continuously flowed over the microwave-irradiated source of carbon, or the reaction may occur under batch conditions. The source of carbon that is heated by microwave irradiation reacts with the hydrogen to thereby yield one mole of methane for every mole of carbon and every mole of hydrogen. In some embodiments, the applied microwave power for this reaction may vary between about 50 W and about 2000 W, between about 75 W and about 1500 W, or between about 75 W and about 1000 W, or between about 75 W and about 500 W, or between about 75 W and about 200 W. In some embodiments, the temperature of the reaction may be between about 600° C. and about 1200° C., such as between about 800° C. and about 1000° C.

In some embodiments, the method of the present invention accelerates reaction between a source of carbon and a nitrogen oxide having formula NO_(x) wherein x has a value between 0.5 and 3. Suitable nitrogen oxides may be selected from among NO₂, NO, N₂O, N₂O₂, N₂O₃, N₂O₄, N₂O₅, and any combination thereof. The nitrogen oxide may be continuously flowed over the microwave-irradiated source of carbon, or the reaction may occur under batch conditions. Such reaction involves complex equilibria, and the products of such reaction include carbon monoxide, carbon dioxide, nitrogen, nitrous oxide, and nitric oxide, among others. In some embodiments, the applied microwave power for this reaction may vary between about 20 W and about 2000 W, between about 20 W and about 1500 W, or between about 20 W and about 1000 W, or between about 20 W and about 500 W, or between about 20 W and about 200 W, such as between about 20 W and about 100 W. Lower power requirements may be suitable for this reaction since it is exothermic. In some embodiments, the temperature of the reaction may be between about 600° C. and about 1200° C., such as between about 800° C. and about 1000° C.

The method of the present invention is also suitable for mixtures of gases. For example, in some embodiments, the reactant stream may comprise carbon dioxide and water, e.g., steam. In some embodiments, the reactant stream may comprise carbon monoxide and a nitrogen oxide. In some embodiments, the reactant stream may comprise carbon dioxide and a nitrogen oxide. Tertiary and higher combinations are also possible, e.g., carbon monoxide, carbon dioxide, and water, or carbon monoxide, carbon dioxide, and a nitrogen oxide, etc.

In some embodiments, the microwave source will enable underground coal gasification. Underground coal gasification is a process in which coal is converted into a product gas. In this process, the coal is not mined, and in some instances, the coal is too deep for traditional mining methods, such as below about 1200 feet. Instead, oxidants may be injected, through injection wells, into a non-mined coal seam. Oxidant gases may include air or oxygen. The reaction proceeds, and the product gases are brought to the surface through wells drilled from the surface. Microwave radiation is suitable to accelerate or catalyze underground coal gasification reactions, resulting in the products set forth in the following reactions (1)-(4), e.g., methane, hydrogen, carbon monoxide, and carbon dioxide.

EXAMPLES

The following non-limiting examples are provided to further illustrate the present invention.

Example 1 Microwave-Specific Enhancement of the Carbon-Carbon Dioxide (Boudouard) Reaction

Materials

In this example of microwave catalyzation of the Boudouard reaction, the carbon source was steam activated charcoal (50-200 mesh) with a surface area of 992.3 m2/g, which was obtained from Fisher and used as received. The carbon used in the experiments is a granular powder, with observable particle sizes between ˜10 to 300 μm, consistent with the stated mesh size of the material. The material is quite macroporous, as observed under higher magnification, with pores ranging from around 0.25 to 10 μm observable in the image. Gas physiosorption analysis gave a BET surface area of 992.3 m²/g for the activated charcoal. The elemental composition of the activated charcoal was determined from energy dispersive spectroscopy (EDS) measurements. Apart from carbon and surface oxygen (about 7.49% wt %), the largest impurity is potassium, which is present at about 1.57 wt %. Additional impurities includes Na (about 0.18 wt. %), Al (about 0.20 wt. %), Si (about 0.26 wt. %), S (about 0.10 wt. %), Ca (about 0.12 wt. %), and Cu (about 0.20 wt. %). Carbon dioxide (99.9999% purity) was obtained from Airgas and used as received.

Methods

Dielectric measurements were made on an Anritsu 37347E “Lightning E” Vector Network Analyzer. The Nicolson-Ross-Weir (NRW) algorithm is based on the inversion of the Fresnel-Airy formulas expressing the normal reflection and transmission coefficients of a material layer through the wave impedance of the medium and its refraction index. Through these values one can find complex permittivity and permeability of the material in question. The method has the advantage of providing a broadband description of the complex permittivity and permeability. Methodologically, powdered samples of materials are mixed with paraffin and cast in a toroidal cylinder, with the outer diameter the same size as the cavity of the Damaskos solid sample holder, and the inner space the same diameter as the center conductor of the Damaskos sample holder. One gram of paraffin wax was combined with 1 mL of toluene and sonicated until a thick gel formed. At this point, 0.4 g of activated charcoal was added to the gel, and sonicated to insure homogeneity. A Teflon mold of the appropriate configuration was filled with the activated carbon paraffin gel mixture, and placed in a vacuum dessicator to evaporate the toluene. For measuring the permittivity, the sample was placed in the holder, and its thickness and distance from the end of the holder were measured. The toroids are placed in a 7 mm beadless coaxial air guide and the VNA is used to measure the S-matrix parameters, which characterize the microwave absorption and reflection. Great care is applied in tightly fitting the torroids to the dimensions of the coaxial cavity. The S-matrix parameters are used to calculate the complex dielectric constants, the permeability and permittivity, using standard algorithms such as the Nicolson-Ross-Weir and Baker-Jarvis methods. In particular, The S21 and S11 parameters were measured by the Damaskos software, and the data reduction method “Nicolson Ross” was used to determine an initial ε′ value at 2.00 GHz (ε′=7.2). This initial value given by the Nicolson-Ross method was then used as the initial guess in the “Eps From Transmission” data reduction method, as per the Baker-Jarvis's protocol. See Baker-Jarvis, J; Vanzura, E. J.; Kissick, W. A. Improved Technique for Determining Complex Permittivity with the Transmission/Reflection Method. IEEE Transactions on Microwave Theory and Techniques vol. 38 no. 8 1990 1096-1103.

Microwave experiments were carried out in a CEM Discover commercial microwave system under conditions of fixed applied microwave power. To acquire flow (kinetic) and static (equilibrium) data, two reaction systems were designed and built to fit in the microwave cavity. In the flow system, the reactant gas passes up through the catalyst, which is positioned at the center of the microwave cavity. The reactant gas is introduced into the system using a calibrated mass-flow controller. The volume of the product gas stream as a function of time is then determined with a totalizing mass flow meter. The static system for determining equilibrium constant is a closed reactant system that allows the reactant introduction of the gas into an evacuated cell and imitation of microwave irradiation of the same. In both systems, the internal pressure is constantly measured using a transducer, and the temperature of the catalyst surface is measured in-situ using an external pyrometer that is focused on the surface through a germanium window. Both systems have a septum port that allows aliquots to be extracted and analyzed by gas chromatography. Details of the apparatus are provided below.

Data Acquisition and Analysis.

The penetration depth of the microwaves in the carbon at 2.45 GHz was calculated from the values of the real and the imaginary dielectric constant taken from the dielectric measurement. From the real and imaginary values for permittivity the attenuations factor for the electromagnetic radiation propagating through the carbon can be determined using eqn. S1 below, where ω is the frequency of the radiation, ε′ and ε″ are the real and imaginary permittivity's, μ₀ and ε₀ are the free space permittivity and permeability respectively and μ′ is the real part of the permeability, which is set to one for a nonmagnetic material.

$\begin{matrix} {\alpha = {\omega \sqrt{\left( \frac{\mu_{0}\mu^{\prime}ɛ^{\prime}ɛ_{0}}{2} \right)}\sqrt{\sqrt{1 + \left( \frac{ɛ^{''}}{ɛ^{\prime}} \right)^{2}} + 1}}} & \left( {S\; 1} \right) \end{matrix}$

The penetration depth, where the intensity of the propagating radiant drops to 1/e of its initial value is given by eqn. S2.

$\begin{matrix} {D_{P} = \frac{1}{2\alpha}} & \left( {S\; 2} \right) \end{matrix}$

For the carbon samples where, at 2.45 GHz, ε′=6.190(±0.659) and ε″=1.163 (±0.468), the attenuation, α, is found to be 20.42 m⁻¹ yielding a penetration depth of 24.48 mm

Flow Experiments.

Microwave Experiments

CO₂ flowed at a constant rate over the carbon sample, spread out on a quartz frit at the center of the microwave cavity. Using a fixed microwave power, the carbon is heated and the surface temperature measured with an IR pyrometer. The rate of gas evolution in vol/time and the total volume as a function of time are collected by a totalizing mass flow meter. Gas was extracted from the flowing system at one-minute intervals through a septum and analyzed by gas chromatography (gc) (Shincarbon column), which had been calibrated with standard samples of CO and CO₂ to determine the moles of both gas constituents in the reaction.

Microwave System and Flow Experiments:

Into a custom quartz reaction vessel (11 mm I.D.), as seen in FIG. 1, 0.5 grams of activated carbon (Fischer, 50-200 mesh) was loaded on top of a bed of quartz wool (˜0.1 g.). The reaction vessel was first purged with flowing Ar (g) at a rate of approximately 20 ml min⁻¹ for 10 minutes before a steady stream of CO₂ gas was introduced by a mass flow controller at a flow rate of 50 ml min⁻¹ for a minimum of 1 minute prior to initiating microwave irradiation. The product gas flow was sampled at intervals of 1 min for a total of 10 min, from a sample port in line with a flow meter/totalizer (Omega FMA-4300), and analyzed by gas chromatography (HP 5890 Series II, TCD detector, Restec Shincarbon 80/100 column). Each of the varying wattage runs (75 W, 100 W, 125 W, and 150 W) were run in triplicate.

Thermal Experiments

For flow reactions carried out under thermal condition, a reaction tube of the same diameter and having the same mass of carbon, spread out over a quart frit, is brought up to the desired temperature in a Lindberg tube furnace packed with quartz wool to insulate the tube. After the system comes up to temperature, the flow of CO₂ commenced using the mass flow controller. As with microwave experiments, the volume of gas evolved during the reaction was measured using a totalizing mass flow meter. The product gas was sampled at the same one-minute intervals as in the microwave experiment and analyzed by gas chromatography to determine the composition.

Thermal System and Flow Experiments:

0.5 grams of activated carbon was centered into a quartz tube of 11 mm I.D. held in place by plugs of quartz wool (0.1 grams), FIG. 2. The tube was brought up to temperature (850, 900, 950, and 1000° C.) and maintained by a Lindberg tube furnace packed with quartz wool to insulate the tube. As in the microwave experiments the system was purged with Ar (g) at 20 ml min⁻¹ for 10 minutes or until the desired reaction temperature was attained. Once at a steady temperature, as determined by a thermocouple underneath the carbon bed, the flow of CO₂ was started at 50 ml min⁻¹ and allowed to flow for 2 minutes, to compensate for the difference in system volumes. The product gas was sampled at the same 1 minute intervals for a total of 10 minutes and further analyzed by gas chromatography for composition. The volume of product gas was totalized, excluding the 2 minute purge.

Static Experiment

In the evacuated closed reaction cell, with carbon spread out across the bed and situated in the microwave cavity, a fixed volume of CO₂ is introduced with a gas tight syringe. Microwave irradiation is initiated at a fixed power, and the system is allowed to come to equilibrium. Equilibrium is deemed attained when the temperature of the carbon and the pressure cease to change. Samples of the gas are then extracted and the molar composition determined. The partial pressures of the individual gases are determined from the total pressure of the system, which is measured using a transducer, and the mole fraction of the constituents determined through the gc analysis.

Steady State System and Equilibrium Experiments

FIG. 3 depicts the vessel 10 for conducting steady state reactions. Steady state reactions were conducted in a quartz vessel 10 of 24 mm I.D. with a fixed volume of 75.56 ml, equipped with an absolute pressure gauge 20 (Omegadyne PX409) and a 20 mm anti-reflective coated germanium window 30 (Edmund Optics, 8-12 μm).

A high temperature infrared pyrometer (Omega OS554A-MA-6, now shown in FIG. 3) was focused through the germanium window 30 to monitor the temperature of the carbon bed during the experiment. To the vessel 10, 1 gram of activated carbon was placed in the sample position 40 and the vessel 10 was sealed and put under vacuum. The activated carbon surfaces contain adsorbed gases and surface oxides that interfere with precise measurement of K_(p), and therefore must be pre-treated by microwave irradiation at 200 W under N₂ followed by evacuating using a mechanical pumping. This was repeated a minimum of three times before measurements were made. After desorption pre-treatment, the evacuated vessel 10 was filled with 30 ml of CO₂ via gas tight syringe and microwave irradiation (at the applied microwave powers of 75, 100, 125 and 150 W) was initiated. Each experiment was sampled through the sampling port 50 at 10 minute intervals for a total of 60 minutes, whereby a small aliquot (200 μl) of the effluent gas was extracted with a gas tight syringe. The amount (mmoles) of CO and CO₂ contained in the extracted aliquot was quantitatively determined from the peak areas in the chromatogram from a calibration curve determined for each component. The establishment of equilibrium was the time at which the carbon temperature, total pressure of the system and measured quantities of CO and CO₂ was relatively constant, showing only statistical variation.

The establishment of equilibrium was further verified by perturbing the system at equilibrium by the addition of a 10 ml aliquot of CO₂. The system shows an increase in total pressure as would be expected from the increase in the moles of CO₂. Once equilibrium was reestablished, aliquots of the gas were analyzed and the equilibrium constant determined. It was found that, as it should have, it returned to the same value after addition of additional reactant.

The equilibrium constant was determined from the average of the partial pressures of CO and CO₂ collected at three different times after equilibrium was established

Determination of the Equilibrium Constants

To calculate equilibrium constants (K_(p)), partial pressures were calculated from the mole fraction of the constituent and the total pressure using eqn. S3-S6:

$\begin{matrix} {X_{CO} = \frac{n_{CO}}{n_{T}}} & \left( {S\; 3} \right) \\ {X_{{CO}_{2} =}\frac{n_{{CO}_{2}}}{n_{p}}} & \left( {S\; 4} \right) \\ {p_{CO} = {X_{CO} \cdot p_{T}}} & \left( {S\; 5} \right) \\ {p_{{CO}_{2}} = {X_{{CO}_{2}} \cdot p_{T}}} & \left( {S\; 6} \right) \end{matrix}$

With the calculated partial pressures, K_(p) was then calculated by the equilibrium expression described in eqn. S7.

$\begin{matrix} {K_{p} = \frac{p_{{CO}^{2}}}{p_{{CO}_{2}}}} & \left( {S\; 7} \right) \end{matrix}$

The error in Kp was determined from the standard deviation in the average of the partial pressures of the CO2 and CO, through standard propagation error. (S8)

$\begin{matrix} {\sigma_{K_{p}} = \sqrt{{\left( \frac{2p_{CO}}{p_{{CO}_{2}}} \right)^{2} \cdot {\sigma_{CO}}^{2}} + {\left( \frac{p_{{CO}^{2}}}{p_{{CO}_{2}^{2}}} \right)^{2} \cdot \sigma_{{CO}_{2}^{2}}}}} & \left( {S\; 8} \right) \end{matrix}$

From the equilibrium constants, the Free energy (ΔG) of the reaction at each temperature for was calculated using the thermodynamic relationship (S9), where T is the absolute temperature and R the ideal gas constant. Errors in ΔG were calculated from the error in Kp through stand

ΔG=−RT ln K _(p)   (S9)

Product Determination

The total volume of product gas produced as a function of time was determined using a totalizing mass flow meter which records continuously both the rate of gas evolution and the total volume as a function of time. The concentration of CO and CO₂ in moles/ml of the effluent gas was determined through gas chromatography. A small aliquot (50 μl) of the effluent gas was extracted with a gas tight syringe and the quantities (mmoles) of CO and CO₂ contained in the extracted aliquot was quantitatively determined from the peak areas in the chromatogram using an independently generated calibration curve determined for each component. The total number of moles of each gas in the volume of gas generated is determined in the following way. The reactant gas is delivered using a calibrated mass flow controller at rate of 50 ml/min (±1%) while, simultaneously; the total volume of the product produced is measured over time using a calibrated mass flow meter (±1% accuracy). Since the stoichiometry dictates that for every mole of CO₂ consumed two moles of CO are generated, the difference between the volume of the product and the volume of the reactant produced during the same increment of time must equal ½ the volume of CO produced: V_(prod)−V_(react)=½V_(CO). Therefore, the V_(CO)=2(V_(prod)−V_(react)) and V_(CO2)=V_(prod)−V_(CO). Multiplying the volume of each component with concentration of that component acquired from gc analysis yield the total moles of each component contained in that particular volume increment. These amounts are totaled over time to generate the kinetic plots. The calculated percentages of CO and CO₂ in the total volume collected at each time interval were then calculated using the determined volume fractions.

Data Analysis

Rate constants were determined from a linear regression fit of the steady-state region of the concentration versus time plot. For the microwave-driven experiment, this occurs after ˜300 sec—after the initial outgassing process is completed as below. For the thermal reaction, the entire curve is fit as any outgassing process takes place before the reactant is introduced.

To determine what product gases were emitted due to gases adsorbed to the surface of the carbon, kinetic data was collected using the same protocol as was used on the kinetic CO₂ study but in this case N₂ was flowed over the system.

Aliquots of the gas stream were collected over time and compositionally analyzed. The emitted gases were CO₂, CO and H₂ whose evolution time was dependent on the applied power. See FIG. 4, which provides graphs of the product gases evolved over time from the activated carbon in a flowing N₂ stream at 75, 100, 125 and 150 Watts of applied microwave power. The gases are H₂ (solid line -), CO (dashed line - -), and CO₂ (dashed line with dots -•-). These products are expected for CO₂ and H₂O adsorbed on the surface, which react through the steam-carbon, Boudouard and water-gas-shift reaction, all of which take place readily on the carbon surface. See Walker, P. L.; Rusinko, J. R.; Austin, L. G. In Adv. in Catal; Eley, D. D., Selwood, P. W., Weisz, P. B., Eds.; Academic Press: NY, 1959; Vol. XI, p 133.

Activation Energy. The activation energy was determined by a weighted least squares fit of the natural log of the rate of CO production to the reciprocal of the temperature.

Regression Analysis

Linear regression analysis was used to determine the activation energy (E_(a)) from the Arrhenius equation and the standard reaction enthalpy (ΔH^(o)) from the Van't Hoff equation. The regression analysis was carried using the Stata suite of statistical software. Since both the thermal and microwave data show progressively larger standard deviations as the temperature decreased, we elected to perform the analysis using a weighted linear regression to take this into account. The weighting factor was the standard error, which is the reciprocal of the square of the standard deviation of the dependent variable (s=1/σ²).

a. Arrhenius Fit

Microwave:

R²=0.9980; 95% confidence interval of E_(a) between 61.7 and 33.3 kJ/mole

Thermal:

R²=0.9995; 95% confidence interval of E_(a) between 126.1 kJ and 110.8 kJ/mole

b. Van't Hoff Fit

R²=0.9812; 95% confidence interval of ΔH between 47.4 and 19.3 kJ/mol

Van't-Hoff Equation. The enthalpy (ΔH) was determined by a weighted least squares fit of the natural log of the experimentally determined equilibrium constant versus the reciprocal of the temperature.

Thermochemical Calculations.

For the thermal reaction, the thermodynamic parameters, specifically ΔH and ΔS, were calculated using standard thermodynamic tables. The enthalpy and entropy were corrected for temperature using the heat capacities of the reactants and products to better match the temperatures at which the microwave reaction was experimentally determined. The free energy and equilibrium constant were, in turn, computed from ΔH and ΔS using the standard thermodynamic relationships.

The determination of ΔH and ΔS for the Boudouard reaction is taken from the standard state heats of formation for the products and reactants, contemporary values of which are available through the NIST web site, with the primary source being the NIST-JANAF Thermochemical Tables. See http://webbook.nist.gov/chemistry/ and Chase, M. W. NIST-JANAF Thermochemical Tables, Fourth Edition, J. Phys. Chem. Ref. Data, Monograph 9, 1998, 1-1951.

For the Boudouard reaction (rxn S1) the product is CO and the reactant CO₂ with C assumed to be the element in its natural state (ΔH_(f) ^(o)=0).

CO₂(g)+C(s)⇄2CO(g)   (S1)

From the tables the following thermochemical data was used in our calculations.

CO

ΔH_(f) ^(o)=−110.53 kJ/mole S^(o)=197.66 J/mole K (1 atm, 298 K)

The temperature dependence of the heat capacity from 298-1300 K is:

C _(p) =A+BT′+CT′ ² +DT′ ³ +E/T′ ²

A=25.567; B=6.096; C=4.055; D=−2.6713; E=0.13192 T′=T(K)/1000

CO₂

ΔH_(f) ^(o)=−393.51 kJ/mole S^(o)=213.79 J/mole K (1 atm, 298 K)

The temperature dependence of the heat capacity from 298-1300 K is:

C _(p) =A+BT′+CT′ ² +DT′ ³ +E/T′ ²

A=24.99735; B=55.1870; C=−33.69137; D=7.9484; E=−0.136638 T′=T(K)/1000

C

For carbon we assume graphite, which is typically used in gas-carbon thermochemical calculations and will, by definition, have a zero heat of formation under standard conditions. This is of course, not strictly true since we are using activated charcoal, which is a mixed phase material with graphitic and amorphous phases. The error in assuming graphite, even at higher temperatures, is small since other forms of pure carbon do not have significantly higher heats of formation. For example, diamond is around 2 kJ/mole and coal chars around 6 kJ/mole; all well below the gas phase reactants and products.

ΔH_(f) ^(o)=0; S^(o)=5.6 J/mole K

The temperature dependence of the heat capacity of graphite from 250-3000 K. See Butland, A. T. D.; Maddison, R. J. J. Nuc. Mater. 49, 1973, 45-56.

$C_{p} = {A - {BT}^{\prime} + {CT}^{\prime 2} - \frac{D}{T^{\prime}} - \frac{E}{T^{\prime 2}} + \frac{F}{T^{\prime 3}} - \frac{G}{T^{\prime 4}}}$

A=2.268230080; B=0.01015318728; C=0.3777001400; D=0.1817918712; E=0.06665488560; F=0.006011905920 T′=T(K)/1000

ΔH, ΔS, ΔG and ln(K_(p)) Under Standard Condition (1 atm, 298 K).

ΔH ^(o)=2(ΔH _(f) ^(o))_(CO)−(ΔH _(f) ^(o))_(CO2)=172.5 kJ/mole

ΔS ^(o)=2(S ^(o))_(CO)−(S ^(o))_(CO2)−(S ^(o))_(C)=0.1759 kJ/mole K

ΔG ^(o) =ΔH−TΔS=120.0 kJ/mole

ln(Kp)=−ΔG/RT=−48.4

Temperature Dependence of the Thermodynamic Quantities

The temperatures of the carbon for which equilibrium constants were determined under microwave irradiation ranged from 1085 to 1265 K. To achieve the most accurate comparison possible between microwave and thermal thermodynamic properties were calculated in this temperature range using the heat capacities, though for gas phase reactions these corrections are typically minor. See Benson, S. W. Thermochemical Kinetics, 1976, Wiley, New York.

Δ C_(p) = 2(C_(p))_(CO) − (C_(p))_(CO₂) − (C_(p))_(C) Δ H = Δ H⁰ + ∫₂₉₈^(T_(final))Δ C_(p) ${\Delta \; S} = {{\Delta \; S^{0}} + {\int_{298}^{T_{final}}{\frac{\Delta \; C_{p}}{T}{T}}}}$

At 1085 K, ΔH=182.3 kJ/mole and ΔS=0.19347 kJ/mole K

At 1265 K, ΔH=184.2 kJ/mole and ΔS=0.19503 kJ/mole K

Consistent with the general assumption that the enthalpy is constant, there is only c.a. 2 kJ difference between in the enthalpy over the temperature range of interest. We use the intermediate values of 183.3 and 0.1943 kJ/mole the enthalpy and entropy respectively (Table 2) for all calculations.

2. Results and Discussion

Microwave Absorption and Heating Processes

The volumetric heating of carbonaceous materials by microwave radiation at 2.45 GHz generally proceeds efficiently, depending on the type of carbon. Studies of dielectric relaxation processes in different kinds of carbon have indicated that heat is produced primarily through space-charge (interfacial) polarization, which is typical for solid dielectric materials. See Atwater, J. E.; Wheeler, R. R. Complex Permittivities and Dielectric Relaxation of Granular Activated Carbons at Microwave Frequencies Between 0.2 and 26 GHz Carbon 2003, 41, 1801-1807; Atwater, J. E.; Wheeler, R. R. Microwave Permittivity and Dielectric Relaxation of a High Surface Area Activated Carbon Appl. Phys. A, 2004, 79, 125-129; Atwater, K. E.; Wheeler, R. R. Temperature Dependent Complex Permittivities of Graphitized Carbon Blacks at Microwave Frequencies Between 0.2 and 26 GHz J. Mater. Sci. 2004, 39, 151-157; Challa, S.; Little, W. E.; Cha, C. Y. Measurement of the Dielectric-Properties of Char at 2.45 Ghz J. Microw. Power Electromagn. Energy 1994, 29, 131-137; and Hotta, M.; Hayashi, M.; Lanagan, M. T.; Agrawal, D. K.; Nagata, K. Complex Permittivity of Graphite, Carbon Black and Coal Powders in the Ranges of X-band Frequencies (8.2 to 12.4 Ghz) and between 1 and 10 GHz ISIJ Int. 2011, 51, 1766-1772. Qualitatively, this loss mechanism arises from charge carriers (electron-hole pairs) that become trapped at the surface in defect and impurity sites and grain boundaries. The trapping process impedes the recombination charge, thereby dephasing the charge transport from the oscillating electric field and resulting in dielectric loss. The loss process is measured through the imaginary part of the dielectric constant, ε″, (equation 1) with the magnitude of the loss often given through the loss tangent (equation 2). See Metaxas, A. C.; Meredith, R. J. Industrial Microwave Heating; The Institution of Engineering and Technology: London, 1983.

ε=ε′−iε″  (1)

tan δ=ε″/ε′  (2)

The magnitude of the loss, and hence the degree of heating, varies among different types of carbon. Carbon activated at high temperature, for example, tends to heat extremely efficiently in the microwave. There is a small maximum in the loss tangent (tan δ) quite close to the excitation wavelength of the microwave oven, with the loss tangent having a value of 0.18 (±0.06) at 2.45 GHz. It is important to note, however, that the dielectric loss tends to increase as a function of temperature for activated charcoals. From the values obtained for the components of the dielectric constant at 2.45 GHz, the attenuation factor for the microwaves propagating through the carbon was 20.42 m⁻¹, which yields a penetration depth, D_(p), of 24.5 mm. In the experiments carried out in the study, the diameters of the carbon samples used were 24 mm for the static and 11 mm for the flow experiments. Because the radiation comes in uniformly from all sides, we would not expect to see significant attenuation of temperature at the centers of the samples.

The actual uniformity of the microwave heating of the carbon under microwave irradiation was assessed using thermal imaging, collected while looking down the reaction tube directly at the surface of the carbon (1 g, 24 mm diameter) through a germanium window. Consistent with volumetric heating of the sample, the surface of the carbon exhibits the highest temperature at the center, which decreases toward the edges of the cell, where convective heat transfer to the surroundings is greatest. While the temperature across the surface generally increases in going from the edge to the center, it is not completely uniform, with variations and hot spots observable in regions of the surface. Such heterogeneity, which is often transitory, is not uncommon for microwave heating of solids and can arise from a number of factors, including defect and impurity sites. In our studies, the temperature of the surface of the carbon was collected using an IR thermometer, which averages the temperature over a 13 mm area of the carbon. The presence of these transitory hot spots contributes to observed temperature fluctuations, even under steady-state conditions.

As discussed, the Boudouard reaction (rxn 3), because it is endothermic, requires high temperatures to drive the equilibrium substantially to the right and produce any significant amount of CO. Our hypothesis is that microwave heating of the carbon may result in a more facile generation of CO with much lower energy expenditure. The rationale for this arises from two properties unique to microwave heating. One is simply based on selective heating, by which the microwaves will selectively heat the carbon to the point where the reaction occurs without the necessity of heating the entire system. The second is the possibility of a microwave-specific enhancement due to the space-charge heating mechanism that is intrinsic to microwave heating of carbonaceous solids.

Kinetic Studies

The reaction under conditions of flowing CO₂ was carried out in a quartz reactor system, with activated carbon (0.5 g) spread out evenly across an 11-mm diameter quartz frit. The sample was positioned in the center of the microwave cavity, with CO₂ flowing up through the carbon at 50 ml/min via a mass flow controller. The volume of the gaseous reaction product was measured using a mass flow meter, with the molecular compositions determined through gas chromatographic (gc) analysis. Under these conditions, the internal pressure remained close to ambient through the duration of the run. For comparison purposes, the reaction was also carried out under conventional convective heating in a thermostatically controlled tube furnace, using identical conditions of sample size, mass, and reactant flow. Importantly, although we have endeavored to match as closely as possible the reaction conditions in the microwave and convective thermal reactor, in the convective thermal reactor, both the carbon and the gas phase reactant and product will always be at the same temperature while in the microwave, the carbon surface will be at a significantly higher temperature than the gaseous medium. Finally, while both the microwave and convectively-heated reactions are inherently thermal in nature, we distinguish between them in this report by referring to them as “microwave” and “thermal,” respectively.

The production of CO from the reaction of CO₂ with carbon under microwave and thermal conditions as a function of time is shown in FIG. 5A and FIG. 5B, respectively, which are graphs depicting the production of CO from the reaction of CO₂ with carbon as a function of time under (FIG. 5A) microwave and (FIG. 5B) thermal conditions. Under microwave irradiation (FIG. 5A), we observe a rapid evolution of CO in the very early stages of irradiation; however, after approximately 300 sec, the rate decreases and becomes constant, commensurate with the steady-state production of CO. The origin of the initial, rapid flux of product gas is due to adsorbed species that are present on the surface of the activated charcoal prior to initial heating. This was verified by measuring the microwave-induced gas evolution from the activated carbon under a flow of inert gas. The species evolved include CO, CO₂, and H₂, which can come from the reaction of carbon with adsorbed CO₂, CO, and H₂O. The evolution of these species falls to negligible amounts (≦10⁻⁷ moles) after approximately 300 sec under 75 W of irradiation and more quickly at higher powers.

The rate of CO production under microwave conditions, obtained from least-square fitting of the linear, steady-state portion of the data, after the initial outgassing of adsorbed species, is quite reproducible over independent runs and increases systematically with increasing power/surface temperature (Table 1). At the highest power level, 150 W, we observed that the rate of CO production was almost unchanged from that at 125 W (1.56 versus 1.50 mMole/min, respectively) (FIG. 5A). Analysis of the product distribution indicates that at the highest power, virtually all of the CO₂ is consumed, suggesting that at that power under this flow rate, the reaction is mass-limited. Increasing the flow of CO₂ to 75 mL/min in fact yielded an increase in the production of CO above the mass restrictions of the 50-mL/min flow rate. The higher flow rate yielded a rate of CO production of 1.66 mMol/min, which was consistent with the rate versus temperature trend observed for the lower power setting.

TABLE 1 Rate of CO evolution under microwave and thermal conditions Microwave Thermal Arrhenius E_(a) = 38.5 (±1.22) kJ/mole E_(a) = 118.4 (±1.8) kJ/mole Parameters A = 1.09 × 10⁻³ (±0.13) A = 1.57 (±0.08) sec⁻¹ sec⁻¹ Applied Temper- Power Temperature Rate ature Rate (W) (° C.) (mMol/min) (° C.) (mMol/min) 75 813 0.908 (±0.10)  850 0.291 (±0.010) 100 912 1.32 (±0.04) 900 0.549 (±0.074) 125 958 1.50 (±0.11) 950 0.804 (±0.031) 150 992  1.66 (±0.07)* 1000 1.30 (±0.02)

The production of CO under thermal conditions is shown in FIG. 5B. As can be seen in FIGS. 5A and 5B, product formation is quite linear with time. We do not observe the initial outgassing process that is observed in microwave heating because the carbon is brought up to the desired temperature under an inert atmosphere prior to flowing CO₂ over it. The rates of reaction obtained under thermal conditions are shown in Table 1. As would be expected, they increase steadily as a function of temperature. In addition, they are generally more reproducible over independent runs, as indicated by the small standard deviation of the rates compared to those of the microwave-driven reaction.

In comparing the two processes, it is clear that over the range of temperatures studied, the microwave-driven reaction is faster than the equivalent thermal reaction. The difference between the microwave and thermal reaction is more pronounced at lower temperatures, where the microwave-driven reaction is over three times faster than the thermal reaction. The difference in rates decreases until, at the highest temperature used, the microwave rate is only 1.4 times faster than the thermal reaction. This behavior suggests that the two modes of driving the reaction must have fundamentally different temperature dependencies of their rate constants, which should be manifested in the Arrhenius parameters. FIG. 6 shows Arrhenius plots for the thermal and microwave-driven reactions, based on the temperatures and rates given in Table 1. Good linear fits were obtained for both sets of data, from which the apparent activation energy for the microwave and thermal process was found to be 38.5 and 118.4 kJ/mole, respectively.

By equating the Arrhenius equations for the thermal and microwave process, 1049° C. is found to be the temperature at which both processes generate CO at the same rate; above that temperature, the thermal process is more efficient while below it, the microwave process is more efficient. Clearly, the reaction under microwave conditions has a significantly lower apparent activation energy than it does under thermal conditions.

This suggests that the interaction of the microwaves with the carbon does more than just act as a source of selective heating; it in fact yields different energetics of the rate-determining processes occurring at the surface. Moreover, the pre-exponential factor for the microwave-driven reaction is significantly smaller, by three orders of magnitude, than it is for the thermal reaction. While we will not attempt to fully analyze the meaning of this difference, it is reasonable to suggest that because the temperature of the gas in the microwave experiment is significantly lower than it is in the thermal experiment, it will have a smaller collision frequency with the surface, thereby contributing to the lower pre-exponential term.

The composition of the generated gas, measured as a function of time and temperature, was determined for both the microwave (See FIG. 7A) and thermal reactions (See FIG. 7B). Experimentally, for the microwave-driven reaction, the flow of CO₂ began, and microwave power was applied. There is a slight induction period where CO increases relative to CO₂ as the carbon is exposed to the microwave radiation. However, steady-state conditions appear to be attained at times greater than ˜400 sec, depending on the applied power, with the amounts of CO and CO₂ becoming relatively constant. The exception to this generalization is the 75 W experiments, which are less reproducible, as indicated by the larger standard deviation, and which show variation in CO and CO₂ composition that deviated from steady-state conditions. Experiments run at 50 W of applied microwave power resulted in erratic CO production; reproducible kinetic data could not be attained. As such, 75 W of applied power in our system approximately represents a lower limit for the microwave-specific effect in our system. In the case of the thermal reaction, the sample is already at temperature when the flow of CO₂ commences, and no induction period is observed; the composition of gas is already established when the initial data point is collected at 60 sec. For the thermal reaction, there is a slight decrease in the CO (and concomitant increase in CO₂) with time, the origin of which is not completely known. At the higher temperatures, steady-state conditions are ultimately attained by 600 sec; however, at some of the lower temperatures, small decreases (<0.3%/min) in the CO are still evident. Thus, the values at 600 sec should be viewed as an upper limit of the steady-state CO composition.

Consistent with the known thermodynamics of the reaction, the amount of CO produced increases with increasing temperature as the equilibrium is shifted to the right; this trend is observed in both the thermal and microwave processes. What is clear, however, and with reference to FIG. 7B, when comparing the two modes of reaction, is that when steady-state conditions are reached, the microwave-driven reaction will tend to generate more CO than is observed under thermal conditions at similar temperatures. As predicted from the Arrhenius equations for the two processes, we expect the rate of CO production to be greater in the microwave at lower temperatures, with the rates of the two processes converging as the temperature approaches 1049° C. At the lowest temperature, i.e., 813° C. for the microwave process and 850° C. for the thermal process, the microwave process generates over three times more CO than the thermal process. Producing CO at the same rate as we do with the microwave at 813° C. (75 W) would require 960° C. under conventional thermal conditions.

Equilibrium Studies

The differences in the rate of product formation and in the apparent activation energy observed in the kinetic studies indicate that the effect of microwave radiation on the reaction goes far beyond simple selective heating and may exhibit different thermodynamics for the reaction. Because the Boudouard reaction is reversible, as are other carbon gasification reactions, the determination of the equilibrium constants under microwave irradiation at various powers will yield the primary thermodynamic quantities associated with the process. See Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976; and Lewis, G. N.; Randall, M. Thermodynamics, 1st ed.; McGraw-Hill: London, 1923. In these experiments, one gram of carbon covering a 24-mm diameter was irradiated in a completely sealed vessel, which was evacuated and charged with CO₂ to a predetermined pressure. The pressure of the vessel and the temperature of the carbon surface were monitored in situ using a transducer and an IR thermometer, respectively. Samples of the gas were extracted and analyzed by gc over the course of the reaction to determine their concentration when equilibrium was attained.

The system reached equilibrium at approximately 40 min of irradiation when the temperature, total pressure, and composition reach relatively constant values. It was further verified by control experiments that the system was in chemical equilibrium, and the equilibrium was perturbed by the addition of CO₂ to the system, which resulted in re-equilibration to the same value for the equilibrium constant. The values of the equilibrium constants, determined from these measurements using the equilibrium expression K_(p)=(P_(CO))²/P_(CO2), are shown in Table 2. The equilibrium constants for the thermal reaction as a function of temperature were reported previously. See Walker, P. L.; Rusinko, J. R.; Austin, L. G. Gas Reactions of Carbon. In Advan. Catal.; Eley, D. D., Selwood, P. W., Weisz, P. B., Eds.; Academic Press: NY, 1959; Vol. XI; pp 133-221. The reported values were obtained from the free energy change, ΔG^(o), of the reaction as a function of temperature, calculated using the standard state heats of formation, ΔH_(f) ^(o), and standard entropies, S^(o), of the products and reactants at 298 K. To provide a quantitative comparison between the thermochemical properties of the microwave and thermal reaction, we have calculated the free energy change and the equilibrium constant using contemporary thermodynamic data (ΔH_(f) ^(o) and S^(o)). The data was temperature-corrected using the appropriate heat capacities to match the temperature of the carbon surface measured in the microwave experiments.

TABLE 2 Equilibrium constants and thermochemical parameters Microwave T (K) ΔG ΔH T (K) Gas^(a) K_(p) (kJ/mol)^(b) (kJ/mole) ΔS (J/mole) 1086 267 68.3 (±10.6)  −38.1 (±1.3)  1185 380 85.2 (±9.1)   −43.8 (±1.0)  33.4 (±3.3) 65.6 (±3.1) 1232 390 103 (±6.66) −47.5 (±0.64) 1265 404 111 (±0.17) −49.6 (±0.02) Thermal^(c) T (K) K_(p) ΔG (kJ/mol) ΔH (kJ/mole) ΔS (J/mole) 1086 21.6 −27.7 1185 117.43 −47.0 183.3 194.3 1232 238.7 −56.1 1265 380.7 −62.5 ^(a)estimated using the ideal gas equation; ^(b)calculated from ΔG = −RTlnK_(p), where R is the ideal gas constant; ^(c)all tabulated thermodynamic quantities and equilibrium constants were calculated from standard thermochemical data.

The difference in these thermodynamic quantities of the reaction can be seen in Table 2. It is clear from the data that the equilibrium constants for the microwave process are larger, so the ΔG of the reaction is more negative than the thermal process at the lower end of the temperature range. The trend in the equilibrium constants of the two processes as a function of temperature is shown in FIG. 8. Clearly, the microwave-driven reaction has significantly weaker temperature dependence than does the thermally-driven reaction. Because the temperature dependence of Kp and ΔG is dictated by the values of ΔH and ΔS, there must be a significant difference in these quantities with the two methods of heating.

Because the enthalpy of the Boudouard reaction varies only slightly with temperature due to the small temperature-dependent heat capacities of CO and CO₂, we can estimate the enthalpy of the microwave-driven reaction from a Van't Hoff plot (ln(Kp) vs 1/T). The value of ΔH obtained from the slope of the plot was 33.4 kJ/mole, and the value calculated for the thermal reaction was 183.3 kJ/mole (Table 2). Although both values were positive, consistent with the endothermic nature of the Boudouard reaction, the enthalpy change under microwave irradiation was approximately five times lower than that for the thermal reaction. Using the values obtained for the free energy and enthalpy, the entropy change, ΔS, was also determined (Table 2) and was significantly lower in the microwave-driven process.

Clearly, under microwave irradiation, the apparent thermodynamics of the reaction changes profoundly. The fact that the microwave-driven reaction has a negative ΔG at lower temperatures than the thermal reaction arises from its significantly lower value of ΔH, as ΔH will be less than −TΔS at lower temperatures. Conversely, the lower entropy means that as the temperature increases, the thermal process will become more favorable much more quickly than the microwave process as −TΔS_(therm)>−TΔS_(micro). When equating the thermodynamic relationship, ΔG=ΔH−TΔS, for the two processes, the temperature at which both processes have the same value for ΔG is 1164 K; above that temperature, the thermal process is more favorable for producing CO, and below it, the microwave process dominates.

The plots of the mole fraction of CO and CO₂ present at equilibrium as function of temperature were determine from the temperature dependence of the equilibrium constants by noting that, at one atmosphere, which is close to our working pressure, the equilibrium constant in terms of partial pressures is equal to the equilibrium constant in terms of the mole fraction.

$K_{p} = {\frac{\left( P_{CO} \right)^{2}}{P_{{CO}_{2}}} = {\frac{\left( {X_{CO}P_{total}} \right)^{2}}{X_{{CO}_{2}}P_{total}} = {\frac{\left( X_{CO} \right)^{2}P_{total}}{X_{{CO}_{2}}} = {{K_{x}{\mspace{11mu} \;}{for}\mspace{14mu} P_{total}} = {{1\mspace{14mu} {{atm}.\mspace{20mu} X_{CO}}} = {{{- \frac{1}{2}}K_{x}} + {\frac{1}{2}\sqrt{\left( K_{x} \right)^{2} + {4K_{x}}}}}}}}}}$ $\mspace{20mu} {K_{x} = ^{\frac{{\Delta \; H} - {T\Delta S}}{R \times T}}}$

Using thermodynamic relationships, the equilibrium constants can be determined over a wide range of temperatures for the two processes. From this, we can plot the predicted mole fraction of CO and CO₂ that will be present at a given temperature. See FIG. 9, which is a plot showing the mole fraction of CO and CO₂ as a function of temperature for the microwave (solid line -) and thermal (dashed line - -) Boudouard reaction, predicted from the calculated equilibrium constants and assuming one atmosphere of pressure. Significantly, based on our thermodynamic calculations, the crossover temperature at which CO becomes the favored (i.e., ΔG<0) species occurs at 643° C. in the thermal reaction and 213° C. in the microwave reaction. These temperature values are calculated from the thermodynamic values. In practice, one may employ higher temperatures to ensure the reaction proceeds toward the desired product. Accordingly, the microwave may be used at 800° C., while a thermal reaction may need to use temperatures around 1000° C. to achieve the product. Moreover, the temperature at which the desired CO product would account for ≧90% of the product is 419° C., while it is necessary to reach 763° C. under conventional convective thermal heating. This suggests a rather pronounced advantage for the use of microwaves to drive this reaction. And in addition to the thermochemical effect, the heat required to run the reaction in the microwave is significantly less because it is not necessary to heat the entire system. Table 2 shows that the average temperature of the gas medium in our reactor system during the equilibrium measurements, estimated from the ideal gas law, is lower than the carbon surface by more than 800° C. With the microwave driven reaction it is not necessary to heat the entire system, which suggests a large energy benefit to driving the reaction in that manner. Conversely, the lower temperature of the gas and its concomitant lower kinetic energy may affect how readily equilibrium conditions can be attained.

The data clearly shows that a microwave-specific effect exists and that it affects very fundamental aspects of the reaction. Although the origin of the effect has not been experimentally investigated, we should consider whether plasma formation plays a role in the process, as has been both suggested and actively utilized in prior studies of microwave applications for gas-carbon processes. See Djebabra, D.; Dessaux, O.; Goudmand, P. Coal-Gasification by Microwave Plasma in Water-Vapor Fuel 1991, 70, 1473-1475; and Menendez, J. A.; Dominguez, A.; Fernandez, Y.; Pis, J. J. Evidence of Self-Gasification During the Microwave-Induced Pyrolysis of Coffee Hulls Energy Fuels 2007, 21, 373-378. Plasmas are relatively easily formed in the microwave, although typically not at the low powers employed in our studies.

The approximate magnitude of the microwave-specific enhancement can be determined from thermodynamic consideration. The enthalpy of the reaction can be determined in the standard way from the standard enthalpies of the products and reactants at the reaction temperature, T, (equations 3-4). For the thermal reaction, this is the difference in the product and reactant, including the relevant stoichiometry factors (equation 3).

ΔH _(thermal)=2(ΔH ^(o) _(T))_(CO)−(ΔH ^(o) _(T))_(C)−(ΔH ^(o) _(T))_(CO) ₂   (3)

ΔH _(microwave)=2(ΔH ^(o) _(T))_(CO)−(ΔH ^(o) _(T) +ΔH ^(o) _(MW))_(C)−(ΔH ^(o) _(T))_(CO) ₂   (4)

ΔH_(thermal)−ΔH_(microwave)≈(ΔH^(o) _(MW))_(C)   (5)

For the gas phase reactant and products, it is assumed that even though the average temperature of the gas in the medium is much lower in the microwave experiment (Table 2), the temperature of the gas equilibrates rapidly with the carbon surface when the reaction takes place. As such, the enthalpies are the same in both processes. For the carbon, because it directly absorbs microwaves, the enthalpy can be written as the sum of the thermal enthalpy and the contribution enthalpy due to the microwave-specific contribution (equation 4). The magnitude of the microwave-specific enthalpy is the difference between the thermal and microwave reaction enthalpy (equation 5), which for our system is 149.9 kJ/mole.

This thermodynamic quantity likely represents a change in the surface energy of the carbon brought about by the mechanism of microwave heating. See Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; John Wiley & Sons: New York, 1994. It is reasonable to postulate that this effect arises from the space-charge mechanism, by which the microwave radiation heats the carbon.

In particular, the oscillating electric field vector of the incident radiation creates transient electron-holes pairs, the hindered recombination of which represents one of the primary loss processes that lead to heating. Under constant radiation, a steady-state concentration of these electron-hole pairs will exist on the surface or will be trapped at defect or impurity sites. The initial step in the Boudouard reaction involves oxygen transfer to the surface, oxidizing one of the carbon sites with concomitant ejection of CO, which is shown schematically. See FIG. 10, which depicts the proposed mechanism of the microwave-specific effect on the Boudouard reactions. See Walker, P. L.; Rusinko, J. R.; Austin, L. G. Gas Reactions of Carbon. In Advan. Catal.; Eley, D. D., Selwood, P. W., Weisz, P. B., Eds.; Academic Press: NY, 1959; Vol. XI; pp 133-221; and Ergun, S. Kinetics of the Reaction of Carbon Dioxide with Carbon J. Phys. Chem. 1956, 60, 480-485. The rate-determining step is generally taken to be the rupturing of the oxidized carbon site on the surface and the ejection of CO. There has been considerable study, both experimental and theoretical, of the exact nature of the active carbon site, and FIG. 10 is a schematic of the fundamental processes. See Walker, P. L.; Rusinko, J. R.; Austin, L. G. Gas Reactions of Carbon. In Advan. Catal.; Eley, D. D., Selwood, P. W., Weisz, P. B., Eds.; Academic Press: NY, 1959; Vol. XI; pp 133-221; Ergun, S. Kinetics of the Reaction of Carbon Dioxide with Carbon J. Phys. Chem. 1956, 60, 480-485; Huttinger, K. J. A Method for the Determination of Active-Sites and True Activation-Energies in Carbon Gasification .1. Theoretical Treatment Carbon 1990, 28, 453-456; and Marchon, B.; Tysoe, W. T.; Carrazza, J.; Heinemann, H.; Somorjai, G. A. Reactive and Kinetic-Properties of Carbon-Monoxide and Carbon-Dioxide on a Graphite Surface J. Phys. Chem. 1988, 92, 5744-5749. There are two potential roles where, either separately or in tandem, the microwave radiation can accelerate the reaction. First, chemically, the electron-hole pairs can be viewed as radical anions and cations, respectively. These species are likely to represent an active site that is more reactive to entering CO₂ molecules, with the carbon of the CO possibly favoring the radical anion and the oxygen favoring the cation, thereby enhancing the initial oxidation process. Obviously, because the electron-hole pairs are transitory, this mechanism of enhancement will depend on the steady-state concentration of radicals and the impact frequency of the CO₂ at the surface. Once oxidized, the surface will contain polar groups that can couple with the radiation through typical Debye-type interactions. Selective interfacial heating of these groups can potentially accelerate the desorption of CO from the surface, thereby significantly increasing the rate-determining step for the process. Such interfacial heating effects have been well established in studies by Conner for substrates adsorbed on oxide surfaces. See Conner, W. C.; Tompsett, G. A. How Could and Do Microwaves Influence Chemistry at Interfaces? J. Phys. Chem. B 2008, 112, 2110-2118; and Vallee, S. J.; Conner, W. C. Microwaves and Sorption on Oxides: A surface Temperature Investigation J. Phys. Chem. B 2006, 110, 15459-15470.

Example 2 Microwave-Specific Effects on the Equilibrium Constants and Thermodynamics of the Steam-Carbon and Related Reactions

Materials

Graphite (Fisher, Grade #38), was the carbon source, and it was used as received. The carbon used in the experiments is a granular powder, with observable particle sizes between ˜6 to 60 μm. Gas physisorption analysis gave a BET surface area of 7.6 m²/g for the material. The elemental composition of the activated charcoal was determined from energy dispersive spectroscopy (EDS) measurements. The graphite was pure with C being >99 wt. % C and containing small amount (<0.3 wt %) of Al, Si, Fe and Cu.

Methods

All microwave reactions were carried out in a CEM Discover microwave oven under conditions of fixed applied power. Equilibrium determinations were performed in a specifically designed quartz apparatus, described subsequently, which can be centered in the cavity of the microwave. The steady-state reactions were conducted in a quartz vessel 10 of 24 mm I.D. with a fixed volume of 75.56 ml, equipped with an absolute pressure gauge 20 (Omegadyne PX409) and a 20 mm anti-reflective coated germanium window 30 (Edmund Optics, 8-12 μm). See FIG. 3, which depicts the vessel 10 for conducting steady state reactions. A high temperature infrared pyrometer (Omega OS554A-MA-6) was focused through the germanium window 30 to monitor the temperature of the carbon bed during the experiment.

For the equilibrium experiments, the reaction cell was charged with 1 gram of graphite powder. The sealed vessel was evacuated to <1 mBar and then charged with approximately 450 mBar (35 mL) of N₂ (g). The sample was irradiated for 10 minutes at 200 W of microwave power and then evacuated. This cleaning procedure was repeated twice more for a total of three cleaning cycles to remove any adsorbed water or surface oxide species from the graphite. After the final cleaning cycle, the cell was evacuated and brought to room temperature before slowly being vented to atmospheric pressure using N₂.

While the sample cooled, the deionized (DI) water was added to the static cell using the following technique. Using a micropipette, 30 μL of DI water was pipetted into a small Dewar flask (Lab-Line Thermo-Flask) filled with LN₂. The droplet was frozen and weighed for accuracy of the water addition, 29 mg (1.6 mmol). The static cell was placed in the LN₂ bath and the sphere of ice was placed into the cell, all the while being kept at LN₂ temperatures. The cell was quickly reattached to the apparatus and evacuated to <1 mB while submerged in the LN₂ bath. Once evacuated, the cell was allowed to warm up to room temperature, giving an initial pressure reading of ≈30 mBar.

With the apparatus at room temperature and initial pressure, the cell was irradiated at 200 W to initiate the equilibrium. During irradiation, the cavity of the microwave was continually flushed with air in order to maintain a constant cavity temperature and remove any insulating effect. After about 100 minutes at 200 W, the surface temperature and total pressure of the cell remained constant and were determined to be at equilibrium. Four aliquots of 50 μL were taken, after 10 minutes of constant temperature and pressure, and analyzed by gas chromatography (gc) to determine the gas composition. After the last injection, the microwave power was decreased to 175 W, and after an additional 10 minutes, it was re-equilibrated to constant temperature and pressure, and then again, 4 aliquots of 50 μL were taken and analyzed by gc. This procedure was repeated for 150, 125, and 100 W of microwave power. From the determined gas compositions and recorded total pressure, K_(p) values were calculated for the carbon-steam, homogeneous WGS, Boudouard, and carbon-hydrogen reactions at the five experimental microwave powers.

a. Determination of the Equilibrium Constants

C+H₂O⇄CO+H₂ ΔH=+131 kJ/mol   (1)

CO+H₂O⇄CO₂+H₂ ΔH=−41 kJ/mol   (2)

C+CO₂⇄2CO ΔH=+172 kJ/mol   (3)

C+2H₂⇄CH₄ ΔH=−75 kJ/mol   (4)

To calculate equilibrium constants (K_(p)), partial pressures were calculated from the mole fraction (X) of the constituents (i), determined from the gc analysis, and the total pressure of the system, P_(i)=X_(i)P_(total) with the equilibrium constants for all of the equilibria given by eqn. S1-S4.

$\begin{matrix} {\frac{P_{H_{2}}P_{CO}}{P_{H_{2}O}} = {K_{p}^{s - c}{\mspace{11mu} \;}{steam}\text{-}{carbon}}} & \left( {S\; 1} \right) \\ {\frac{P_{H_{2}}P_{{CO}_{2}}}{P_{CO}P_{H_{2}O}} = {K_{p}^{WGS}\mspace{14mu} {water}\text{-}{gas}\text{-}{shift}}} & \left( {S\; 2} \right) \\ {\frac{\left( P_{CO} \right)^{2}}{P_{{CO}_{2}}} = {K_{p}^{Bou}\mspace{14mu} {Boudouard}\mspace{14mu} {reaction}}} & \left( {S\; 3} \right) \\ {\frac{P_{{CH}_{4}}}{\left( P_{H_{2}} \right)^{2}} = {K_{p}^{s - h}\mspace{14mu} {carbon}\text{-}{hydrogen}}} & \left( {S\; 4} \right) \end{matrix}$

The error in Kp was determined from the standard deviation in the average of the partial pressures of the reactants and products, through standard propagation error.

From the equilibrium constants, the Free energy (ΔG) of the reaction at each temperature for was calculated using the thermodynamic relationship (S5), where T is the absolute temperature and R the ideal gas constant. Errors in ΔG were calculated from the error in Kp through standard error propagation.

ΔG=−RT ln K _(p)   (S5)

Data Analysis

The penetration depth of the microwaves in the carbon at 2.45 GHz was calculated from the values of the real (ε′) and the imaginary (ε″) dielectric constants, taken from the dielectric measurement.

The sample measured must be formed as a toroidal cylinder, with the outer diameter the same size as the cavity of the Damaskos solid sample holder, and the inner space the same diameter as the center conductor of the Damaskos sample holder. A Teflon mold of the appropriate configuration was filled with the activated carbon, then liquid wax was injected to fill the spaces in-between the pieces of carbon and hold it together. For measuring the permittivity, the sample was placed in the holder, and its thickness and distance from the end of the holder were measured. The S21 and S11 parameters were measured by the Damaskos software, estimated values for the carbon (2.45 GHz: ε′=10.14+/−0.29 and ε″=2.62) were imputed into the data reduction method “Nicolson Ross”. The initial value given by the Nicolson-Ross method was then used as the initial guess in the “Eps From Transmission” data reduction method, as per the Baker-Jarvis's protocol.

The enthalpy (ΔH) was determined from the Van't Hoff equation from a weighted least squares fit of the natural log of the experimentally determined equilibrium constant versus the reciprocal of the temperature.

Linear regression analysis was used to determine enthalpy (ΔH^(o)) from the Van't Hoff equation. In all analyses a weighted linear regression was carried using the Stata suite of statistical software. The weighting factor was the standard error, which is the reciprocal of the square of the standard deviation of the dependent variable (s=1/σ²).

b. Van't Hoff Fit

1. Steam-Carbon

ΔH=15.2(±0.8) kJ/mol

R²=0.9915; 95% confidence interval of ΔH between 17.9 and 12.7 kJ/mol

2. Boudouard

ΔH=27.0(±0.7) kJ/mol

R²=0.9983; 95% confidence interval of ΔH between 29.0 and 24.9 kJ/mol

3. Carbon-Hydrogen

ΔH=−9.1(±0.6) kJ/mol

R²=0.9890; 95% confidence interval of ΔH between 10.90 and 7.36 kJ/mol

4. Water Gas Shift

ΔH=−11.4(±0.4) kJ/mol

R²=0.9955; 95% confidence interval of ΔH between 13.6 and 9.96 kJ/mol

Thermochemical Calculations

For the thermal reaction, the thermodynamic parameters, specifically ΔH and ΔS, were calculated using standard thermodynamic tables. The enthalpy and entropy were corrected for temperature using the heat capacities of the reactants and products to better match the temperatures at which the microwave reaction was experimentally determined. The free energy and equilibrium constant were, in turn, computed from ΔH and ΔS, using the standard thermodynamic relationships.

Results

Penetration Depth of Graphite

The volumetric heating of carbonaceous materials by microwave radiation at 2.45 GHz generally proceeds efficiently, making carbon-based reactions particularly amenable to microwave processing. See Menendez, J. A.; Arenillas, A.; Fidalgo, B.; Fernandez, Y.; Zubizarreta, L.; Calvo, E. G.; Bermudez, J. M. Microwave Heating Processes Involving Carbon Materials. Fuel Process. Technol. 2010, 91, 1-8. Studies of permittivity and dielectric relaxation processes in different kinds of carbon, including graphite, have indicated that heat is produced through space charge (interfacial) polarization, which is typical for solid dielectric materials. See Hotta, M.; Hayashi, M.; Lanagan, M. T.; Agrawal, D. K.; Nagata, K. Complex Permittivity of Graphite, Carbon Black and Coal Powders in the Ranges of X-band Frequencies (8.2 to 12.4 Ghz) and between 1 and 10 GHz. ISIJ Int. 2011, 51, 1766-1772; and Atwater, K. E.; Wheeler, R. R. Temperature Dependent Complex Permittivities of Graphitized Carbon Blacks at Microwave Frequencies between 0.2 and 26 GHz. J. Mater. Sci. 2004, 39, 151-157. The loss mechanism arises primarily from the generation and migration of electron-hole pairs by the incident radiation, which becomes trapped at the surface at defect sites and grain boundaries. The trapping process hinders recombination, thereby dephasing the charge transport from the oscillating electric field, resulting in a loss process. The loss process is measured through the imaginary part of the dielectric constant (ε″ in eqn. 1), with the magnitude of the loss often measured through the loss tangent, which is the ratio of the imaginary (ε″) to the real (ε′) dielectric constant (eqn. 2).

ε=ε′+iε″  (1)

tan δ=ε″/ε′  (2)

The real and imaginary parts of the dielectric constant for the graphite used in this study were measured over the relevant frequency range. The largest values for the loss tangent occurred where it peaked around 2.6, 4.5, and 8.5 GHz. At the microwave excitation frequency of 2.45 GHz, the loss tangent was found to be 0.26 (±0.01). From the values of the real and imaginary dielectric constant (10.14(±0.29) and 2.62(±0.16), respectively), we calculated a penetration depth of 19.05 mm.

In the CEM microwave used in these experiments, irradiating occurred radially across the 24 mm diameter of the carbon sample, as expected. We also observed relatively uniform heating of the material, with no significant attenuation in the center of the sample.

Establishing Equilibrium

Since the results depended upon an accurate determination of the equilibrium constants under microwave radiation, it was necessary to establish that equilibrium had been attained. Using the static reaction vessel, charged with graphite and water, the pressure of the vessel and the temperature of the carbon surface were monitored in situ during the course of the reaction. Samples of the gas were extracted and analyzed by gc over the course of the reaction to determine the amount of H₂, CO, CO₂, and CH₄ present as a function of irradiation time. The sample was initially irradiated at 200 W of applied power, yielding a surface temperature of 997 K, with the establishment of equilibrium judged to occur when the pressure, temperature, and composition reached steady-state values. Multiple trials were carried out, and the time to reach a steady state at 200 W was ˜100 minutes in all cases. When the steady state was reached, the atmosphere was analyzed four separate times (approximately once every 5 minutes) with the partial pressures of the constituent species determined. The values of the partial pressures used in calculation of the equilibrium constants were the average of the four steady-state values. This whole process was repeated four times with four independent samples. The compositions at lower temperatures were arrived at in the same system by reducing the applied microwave power and allowing the system to reestablish equilibrium, which took approximately 10 minutes.

To verify that the system was at equilibrium, a separate experiment was performed to show that the equilibrium, once established, would return to the same value of the equilibrium constant when perturbed by the addition of additional reactants or products. In this experiment, the system was brought to equilibrium at 200 W of applied microwave power. The application of microwave radiation resulted in an initial decrease in temperature of the carbon surface as the water was heated and vaporized. Upon achieving constant temperature and pressure, the power was reduced to 100 W, and the system was allowed to re-equilibrate for 30 minutes prior to analysis by gc. The temperature of the graphite surface was 516° C. at this power, and a value of K_(p)=2.90±0.21 was determined from analysis of the constituent gases. After the analyzed products had fully gone through the gc column, the equilibrium constant was determined, and 5 mL of CO (g) was injected into the closed system, leading to an increase in total pressure of ≈70 mB (from 1110 to 1180 mB). Once the CO (g) was introduced, the system was allowed to re-equilibrate for 30 minutes, and the composition was analyzed. The temperature was 515° C., and K_(p) was determined to be 2.66±0.17, which was, within experimental error, the same as determined prior to the addition of CO, suggesting that, under the conditions we were using, equilibrium had been established.

Power Threshold for Microwave-Driven Reactivity

The generation of products from the steam-carbon and related gasification reactions was expected to be dependent on the applied microwave power and, as we observed previously with the Boudouard reaction, there should have been a threshold power below which the reaction would not occur. See Hunt, J.; Ferrari, A.; Lita, A.; Crosswhite, M.; Ashley, B.; Stiegman, A. E. Microwave-Specific Enhancement of the Carbon-Carbon Dioxide (Boudouard) Reaction. J. Phys. Chem. C 2013, 117, 26871-26880. In this particular study, which focused only on the thermodynamics of the reaction as a means to assess the magnitude of the microwave effect, such a threshold was related to whether any products could be produced and whether the equilibrium could be attained in a reasonable period of time, which, in these experiments, was set at 100 minutes. Since, given enough time, any system will ultimately reach equilibrium, this time period, while somewhat arbitrary, reflected the practical experimental limitations of doing very long term exposures in the microwave.

To determine this threshold, a sample cell, charged as described above with water and graphite, was systematically irradiated with applied powers, starting at 10 W and moving up in 5-W increments. At each power level, the system was irradiated for 1 hour, and the composition of the gas was determined. It was found that no product gases (H₂ or CO) were observed until 30 W of applied power, corresponding to a carbon temperature of 373° C., where trace amounts of H₂ were detected. While this represented an approximate minimum energy for the production of H₂ and CO, it was well below a practical threshold for the establishment of equilibrium in a reasonable period of time. It was found that at 90 W, while products were readily observed, the system was far from equilibrium, even after 240 minutes. Upon increasing the power to 100 W (491° C.), equilibrium was attained within 120 minutes. As such, all equilibrium determinations were carried out at ≧100 W, which we viewed as the practical range for the establishment of equilibrium in our system.

Equilibrium and Thermodynamic Properties

The reaction of carbon with steam, which forms the basis of energy production processes such as coal gasification, has been studied experimentally under kinetic conditions using flowing reactor systems. See Blackwood, J. D.; McGrory, F. The Carbon-Steam Reaction at High Pressure. Aust. J. Chem. 1958, 11, 16-33; Gadsby, J.; Hinshelwood, C. N.; Sykes, K. W. The Kinetics of the Reactions of the Steam-Carbon System. Proc. Roy. Soc. Lon. A 1946, 187, 129-151; and Long, F. J.; Sykes, K. W. The Mechanism of the Steam-Carbon Reaction. Proc. Roy. Soc. Lon. A 1948, 193, 377-399. In general, the gas mixture produced from the reaction contains all of the possible species, commensurate with the equilibria shown above (rxn. 1-4). The dominant species are H₂ and CO, with the H₂ coming from the steam-carbon (rxn. 1) and WGS reactions (rxn. 2). The reaction of CO₂ with carbon to produce CO (Boudouard reaction) does not contribute appreciably until high temperatures are reached due to its high endothermicity. Similarly, though for the opposite reason, the production of CH₄ through the hydrogenation of carbon (rxn. 4) is always a very minor pathway, because at the temperatures at which gasification reactions are typically run, the equilibrium lies to the left. In addition, the primary step in the reaction, which is the hydrogenation of the graphite, is known to be extremely slow. See Breisach, P; Marx, P. C. Hydrogen-Graphite Reaction between 360 and 800 Degrees. J. Am. Chem. Soc. 1963, 85, 3518-3519.

We observed a strong microwave-specific effect on the isolated C+CO₂ (Boudouard) reaction (rxn. 3) that resulted in a significantly exothermic shift in the enthalpy of reaction. The changes in the apparent thermodynamics of the reaction were proposed to be the result of specific microwave effects on the mechanism from the interaction of the radiation with the carbon surface. Since the steam-carbon reaction occurs through the same basic mechanism as the Boudouard reaction, it seemed likely that it would also be accelerated due to similar microwave effects.

Equilibrium constants for the steam-carbon reaction system were determined at five different power settings that produced graphite surface temperatures from 764 to 997 K. The distribution of species at equilibrium, as a percent of the total composition, is shown in FIG. 11 for each of the temperatures. FIG. 11 depicts the equilibrium composition of gases (CH₄, CO₂, H₂O, CO, and H₂) as a percent of the total gas and as a function of temperature under microwave irradiation. As can be seen in the graph, as the temperature increased, the amount of syngas, CO and H₂, increased steadily at the expense of the minor constituents—CO₂, CH₄, and H₂O. This trend was consistent with the known thermodynamics of the various equilibria.

The strongly endothermic reactions, the steam-carbon (rxn. 1) and the Boudouard reaction (rxn. 3), had their equilibria shifted to the right, generating more CO and H₂ as the temperatures increased. Conversely, the equilibrium of the WGS (rxn. 2) and the carbon-hydrogen reaction (rxn. 4) shifted to the left with increasing temperature due to the exothermicity of those reactions, thereby contributing to the production of CO and H₂ while depleting CO₂ and CH₄.

Steam-Carbon Reaction

The steam-carbon reaction is the most technologically important of the gas-carbon reactions, as it is used directly for the production of syngas. As such, it was of interest to determine whether the large microwave-derived thermodynamic advantage we observed for the Boudouard reaction would be realized for the steam-carbon reaction. The equilibrium constants and values for the free energy of the steam-carbon reaction, determined under microwave irradiation as a function of the temperature of the graphite, are shown in Table 3. To provide a quantitative comparison between the thermochemical properties of the microwave and thermal reaction, we calculated the free energy change and the equilibrium constant using contemporary thermodynamic data (ΔH_(f) ^(o) and S^(o)), temperature-corrected using the appropriate heat capacities to match the temperature of the carbon surface measured in the microwave experiments. See Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976.

TABLE 3 Equilibrium Constants and Thermochemical Parameters for the Steam-Carbon Reaction Microwave T (K) ΔG ΔH T (K) gas^(a) K_(p) (kJ/mol)^(b) (kJ/mol) ΔS (J/mol) 764 (±4) 293 3.19 (±.53)  −7.4 (±1.0) 832 (±3) 309 3.90 (±.61)  −9.4 (±1.0) 15.2 29.5 ± (0.1) (±0.8) 893 (±2) 321 4.39 (±.43) −11.0 (±.7) 949 (±2) 331 4.95 (±.50) −12.6 (±.8) 997 (±2) 337 5.61 (±.48) −14.3 (±.7) Thermal T (K) K_(p) ^(c) ΔG (kJ/mol) ΔH (kJ/mol) ΔS (J/mol) 764 0.03 23.5 832 0.16 12.8 144.2 158.1 893 0.66 3.12 949 2.07 −5.74 997 4.99 −13.33 ^(a)Estimated using the ideal gas equation; ^(b)calculated from ΔG = −RTlnK_(p), where R is the ideal gas constant; ^(c)all tabulated thermodynamic quantities and equilibrium constants were calculated from standard thermochemical data (see supplementary material).

As the data show, under microwave conditions, the equilibrium laid significantly further to the right, favoring the production of synthesis gas at much lower temperatures than those observed under conventional thermal conditions. A plot of the equilibrium constants as a function of temperature for the microwave and thermal reaction is shown in FIG. 12. As can be seen, the thermal reaction had a rapid drop in the magnitude of the equilibrium constant as the temperature dropped below ˜1000 K, while the decrease was much more gradual under microwave irradiation.

Because the enthalpy of gas-carbon reactions tends to vary only slightly with temperature due to the small temperature-dependent heat capacities of the gas phase reactants, we could estimate the enthalpy of the microwave-driven reaction from a Van't Hoff plot of ln(Kp) versus 1/T. See Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. The value of ΔH obtained from the slope of the plot was 15.2 (±0.08) kJ/mol, while the value calculated for the thermal reaction, in this temperature range, was 144.2 kJ/mol (Table 3). Clearly, under microwave irradiation, the apparent thermodynamics of the reaction changed dramatically. The microwave-driven reaction had a negative ΔG at lower temperatures than did the thermal reaction due to its significantly smaller enthalpy, ΔH, which tended to be less than −TΔS at lower temperatures. Conversely, the lower entropy meant that as the temperature increased, the thermal process became more favorable much more quickly than did the microwave process, as −TΔS_(therm)>−TΔS_(micro). Equating the thermodynamic relationship, ΔG=ΔH−TΔS, for the two processes, the temperature at which both processes had the same value for ΔG was 1003 K; above that temperature, the thermal process was more favorable for producing CO and H₂, and below it, the microwave process dominated.

Boudouard Reaction

Since CO is produced as part of the steam-carbon reaction, and CO₂ is rapidly produced from the WGS reaction, the Boudouard reaction is one of the equilibria present in the steam-carbon reaction. Due to its high endothermicity, this reaction only played a small role in the thermally driven steam-carbon process until very high temperatures were reached. In the microwave, however, it was found to be much more exothermic, so it may play a more significant role by converting CO₂ into CO.

The free energy and associated equilibrium constants for the Boudouard reaction, determined experimentally in the microwave and calculated from the thermodynamic tables over the temperature range probed experimentally, are shown in Table 4. As can be seen, the free energy was negative over the entire temperature range under microwave conditions, while it became negative only at 949 K and above for the thermal reactions.

TABLE 4 Equilibrium Constants and Thermochemical Parameters for the Boudouard Reaction Microwave T (K) ΔG T (K) gas^(a) K_(p) (kJ/mol)^(b) ΔH (kJ/mol) ΔS (J/mol) 764 (±4) 293 2.97 (±.38)  −6.9 (±.8) 832 (±3) 309 4.08 (±.14)  −9.7 (±.2) 893 (±2) 321 5.17 (±.37) −12.2 (±.5) 27.0 (±.7) 43.1 (±1.4) 949 (±2) 331 6.50 (±.24) −14.8 (±.3) 997 (±2) 337 7.83 (±.25) −17.1 (±.3) Thermal^(c) T (K) K_(p) ^(c) ΔG (kJ/mol) ΔH (kJ/mol) ΔS (J/mol) 764 (±4) 0.0048 34.12 832 (±3) 0.050 21.12 893 (±2) 0.29 9.458 180.2 191.2 949 (±2) 1.2 −1.249 997 (±2) 3.6 −10.43 ^(a)Estimated using the ideal gas equation; ^(b)calculated from ΔG = −RTlnK_(p), where R is the ideal gas constant; ^(c)all tabulated thermodynamic quantities and equilibrium constants were calculated from standard thermochemical data (see supplementary material).

The equilibrium constants for the two processes over the temperature range investigated are shown in FIG. 13. As with the steam-carbon reaction, the equilibrium under microwave conditions favored the production of CO at significantly lower temperatures than were possible thermally. From the Van't Hoff equation, we estimated the value of the enthalpy for the microwave-driven reaction to be 27.0 kJ/mol, which is more exothermic; from the free energy and enthalpy, the entropy was found to be 43.1 J/mol. Both of these values were significantly less than those determined for the thermal process. Significantly, both the direction and the magnitude of the microwave effect for the Boudouard reaction were similar to that observed for the steam-carbon reaction.

It was important to compare the equilibrium constants and thermodynamic parameters for the Boudouard reaction in the present study, as part of the steam-carbon system, and those determined independently from investigating the isolated reaction to verify that the values obtained in independent measurements were consistent. It must be noted, however, that the current study was carried out over graphite while the prior study used activated charcoal, so some thermodynamic differences were to be expected. The value of ΔH in the current study was 27.0 (±0.7) kJ/mol, while a value of 33.4 (±3.3) kJ/mol was reported in the prior study. This small, 6.4 kJ/mol enthalpy difference can be accounted for because the current study was carried out at a lower average temperature than was the prior Boudouard study (887 K vs 1192 K). Thermochemical calculations yielded an enthalpy decrease of around 3 kJ/mol between the two average temperatures, bringing the values to within experimental error. The entropy difference between the two studies, however, is more pronounced, with a 43.1 (±1.4) J/mol ΔS obtained in the current study and 65.6 (±3.1) J/mol in the prior study. Thermochemical calculations yielded an entropy difference of ˜3 J/mol between the two average temperatures, which did not completely explain the observed difference. It seems that this difference may well reflect the difference in entropy between activated charcoal and more highly crystalline graphite, though further studies may be required to fully elucidate this.

WGS Reaction

The WGS reaction is generally considered an integral part of the carbon steam reaction, which accounts for production of CO₂ in the product gas (rxn. 2). The reaction is weakly exothermic, and, unlike the other reactions in the steam-carbon system, carbon is not a reactant. Instead, the reaction is thought to be catalyzed by the carbon and, under conditions typical of the steam-carbon reaction, equilibrium is rapidly attained. Among the gas-carbon reactions, however, the WGS reaction is not an independent reaction but can be written as the difference between the steam-carbon and Boudouard reactions (i.e., rxn. 1-3) so that the equilibrium constants are simply related, (K_(sc))(K_(Bou))⁻¹=K_(WGS). Thermodynamically, this means that the enthalpy of the reaction is the difference in enthalpies, ΔH_(wgs)=ΔH_(sc)−ΔH_(Bou), and similarly, the entropy is ΔS_(wgs)=ΔS_(sc)−ΔS_(Bou).

In spite of its lack of independence, the WGS reaction is typically (and historically) included in treatments of the steam-carbon system. As such, we determined the values for the equilibrium constants and thermodynamic parameters, over the temperature range investigated (Table 5) as we did for the other equilibria (Tables 3-4).

TABLE 5 Equilibrium Constants and Thermochemical Parameters for the WGS Reaction Microwave T (K) ΔG ΔH T (K) gas^(a) K_(p) (kJ/mol)^(b) (kJ/mol) ΔS (J/mol) 764 (±4) 293 1.08 (±.2)  −0.47 (±1.1) 832 (±3) 309 0.95 (±.15)  0.35 (±1.0) 893 (±2) 321 0.85 (±.1)  1.22 (±.9) −11.4 −14.1 (±.2)  (±.4) 949 (±2) 331 0.76 (±.08) 2.14 (±.8) 997 (±2) 337 0.72 (±.06)  2.8 (±.7)  Thermal T (K) K_(p) ^(c) ΔG (kJ/mol) ΔH (kJ/mol) ΔS (J/mol) 764 0.267 8.39 832 0.168 12.34 893 0.118 15.88 −36.0 −58.1 949 0.089 19.14 997 0.071 21.92 ^(a)Estimated using the ideal gas equation; ^(b)calculated from ΔG = −RTlnK_(p),where R is the ideal gas constant; ^(c)all tabulated thermodynamic quantities and equilibrium constants were calculated from standard thermochemical data (see supplementary material).

As would be expected for an exothermic reaction, the free energy increased with temperature, so the equilibrium constant favored the products at lower temperatures. This trend was observed in both the thermal and microwave reaction. As can be seen in Table 5, over the temperature range studied, the microwave-driven reaction equilibrium generally laid further to the right, with the free energy becoming negative at the low end of the temperature range studied.

The enthalpy of the reaction under microwave conditions was −11.4 kJ/mol, and the entropy was −14.1 J/mol. Clearly, the presence of the microwaves made the apparent enthalpy of the reaction more endothermic by over 24 kJ/mol and the entropy more positive by 44 J/mol. The thermodynamic advantage provided by the microwaves was only realized at higher temperatures where the small negative entropy caused TΔS<ΔH. As the temperature decreased, the free energy of the thermal reaction became more negative per degree temperature change due to the large entropy. Equating the free energy expressions for the thermal and microwave reaction, it was determined that at 559 K, both processes have the same free energy (−3.51 kJ/mol); below that value, the thermal process dominated.

Carbon-Hydrogen Reaction

The carbon-hydrogen reaction, which initially produces methane, is a minor component of the carbon-gas reaction system. When our system attained equilibrium, small amounts of methane were detected at concentrations that were steady-state over the course of the experiment and decreased with reaction temperature. Values for the equilibrium constant and ΔG for the carbon-hydrogen reaction were calculated (Table 6) and compared to the predicted values of these quantities for the thermal reactions. The data suggest that, under microwave conditions, the free energy is always positive and the equilibrium constant always lies to the reactant side over the temperature range investigated. In contrast, the thermal reaction had negative values of ΔG as the temperature decreased, consistent with the exothermic nature of the reaction.

TABLE 6 Equilibrium Constants and Thermochemical Parameters for the Carbon-Hydrogen Reaction Microwave T (K) ΔG ΔS T (K) gas^(a) K_(p) (kJ/mol)^(b) ΔH (kJ/mol) (J/mol) 764 (±4) 293 0.087 (±.007) 15.5 (±.52) 832 (±3) 309 0.078 (±.002) 17.7 (±.13) −9.1 (±.6) −32.2 (±.9) 893 (±2) 321 0.070 (±.002) 19.8 (±.21) 949 (±2) 331 0.066 (±.001) 21.4 (±.16) 997 (±2) 337 0.062 (±.002) 23.1 (±.25) Thermal T (K) K_(p) ^(c) ΔG (kJ/mol) ΔH (kJ/mol) ΔS (J/mol) 764 5.332 −10.63 832 1.914 −4.49 893 0.871 1.03 −79.7 −90.4 949 0.462 6.09 997 0.284 10.43 ^(a)Estimated using the ideal gas equation; ^(b)calculated from ΔG = −RTlnK_(p), where R is the ideal gas constant; ^(c)all tabulated thermodynamic quantities and equilibrium constants were calculated from standard thermochemical data (see supplementary material).

The enthalpy of the microwave-driven reaction, determined from the Van't Hoff plot, was −9.1 kJ/mol, and the entropy, determined from the free energy and the enthalpy, was −32.2 J/mol. The standard thermodynamic relationship (ΔG=ΔH−TΔS) predicted that, in the microwave, ΔG would remain positive all the way down to 282.6 K, whereas for the thermal reaction, free energy would be negative below 881 K. This is an interesting result, as it means that the reverse reaction, the dehydrogenation of methane, will be favored. In recent years, this dehydrogenation reaction has been of some interest in the production of clean hydrogen fuel. See Abbas, H. F.; Daud, W. M. A. W. Hydrogen Production by Methane Decomposition: A Review. Int. J. Hydrog. Energy 2010, 35, 1160-1190; and Ahmed, S.; Aitani, A.; Rahman, F.; Al-Dawood, A.; Al-Muhaish, F. Decomposition of Hydrocarbons to Hydrogen and Carbon. Appl. Catal. A 2009, 359, 1-24. However, we approached this result with some caution. The forward reaction of hydrogen reacting with carbon is known to be extremely slow, with methane formation rates ranging from 10⁻¹⁶ to 10⁻¹² mol g⁻¹ sec⁻¹ between 600 and 1100 K. See Breisach, P; Marx, P. C. Hydrogen-Graphite Reaction between 360 and 800 Degrees. J. Am. Chem. Soc. 1963, 85, 3518-3519; Wood, B. J.; Wise, H. Reaction Kinetics of Gaseous Hydrogen Atoms with Graphite. J. Phys. Chem. 1969, 73,1348 ff; and Zielke, C. W.; Gorin, E. Kinetics of Carbon Gasification—Interaction of Hydrogen with Low Temperature Char at 1500-Degrees-F. to 1700-Degrees-F. Ind. Eng. Chem 1955, 47, 820-825. As such, we may not have quite attained equilibrium for this reaction. Careful scrutiny of the measured CH₄ concentrations for the data points used to determine the equilibrium constants across the temperature range indicated that, within experimental error, there was no systematic increase in CH₄ generation, suggesting that the system was either at equilibrium or closely approaching it. As such, it is reasonable to suggest that the direction, if not the absolute magnitude, of the microwave effect was likely to be correct.

Discussion

The reaction of primary interest is the steam-carbon reaction, which is highly endothermic and is used commercially to generate synthesis gas. As indicated in the results, there is a clear shift in the equilibrium toward the desired syngas products under microwave irradiation. A more general view of the effect of microwaves on the complex equilibria that make up the gasification reaction system can be estimated from the thermodynamic parameters. In particular, the equilibrium composition in mole fractions of the total reaction system over a broad temperature range can be approximated from the predicted values of the equilibrium constants, written in terms of mole fraction (K_(X)), with the temperature dependence of the equilibrium expression estimated from the thermodynamic parameters (eqn. 3) obtained experimentally for the microwave reaction and calculated for the thermal reaction.

$\begin{matrix} {K_{X} = {^{- \frac{\Delta \; G}{RT}} = ^{- \frac{{\Delta \; H} - {T\; \Delta \; S}}{RT}}}} & (3) \end{matrix}$

By using equation 3 for the temperature dependence of each of the equilibrium constants in rxns. 1-4, the equilibrium expressions can be solved numerically for the mole fractions of each constituent as a function of temperature. FIG. 14 shows the approximate composition of the reactant (H₂O) and products (CO and H₂) of the steam-carbon reactions as a function of temperature for the microwave and thermal process. FIG. 14 depicts equilibrium composition of the reactants and products of the steam-carbon reaction as a function of temperature under microwave (thin lines) and thermal (thick lines) conditions. The reactant is H₂O, solid line. The products are H₂ (dashed line) and CO (dashed line with dots).

As can be seen in the FIG. 14, in the microwave, the consumption of water and generation of hydrogen and carbon monoxide occur at significantly lower temperatures than those required by the thermal process—consistent with the more exothermic nature of the reaction. These calculations predict that hydrogen will reach a maximum at 463 K, whereas under thermal conditions it is expected to occur at 890 K. The calculations predict that, in general, less CO will be produced under microwave radiation, with its production slowly decreasing over the temperature range, while under thermal conditions, its production is on par with that of H₂, peaking at 917 K. The decrease in CO arises because the lower temperatures lead the exothermic WGS reaction to be more favorable, and CO is consumed. As the temperature goes up, the WGS reaction becomes less favorable; however, the Boudouard reaction, which is thermodynamically more favorable under microwave conditions but still endothermic, begins to produce CO from CO₂ at the higher end of the temperature range, yielding the predicted curve. Consistent with this, CO₂ production is greater at low temperatures in the microwave reaction.

Obviously, while these plots provide a good graphical comparison of the difference between microwave and thermal reactivity for the steam-carbon system, the low-temperature regions of the graphs are not accessible due to the threshold power limits of the microwave reactions. In short, while the graphs indicate that we should attain the highest equilibrium concentration of H₂ at 463 K, this is below the threshold where any product would be observed in the microwave. The practical threshold temperatures are indicated by the vertical lines in FIG. 14. The vertical lines (perpendicular to the x-axis) represent microwave thresholds for product formation. The first vertical line represents the lowest temperature (power) at which any H₂ is observed, and the second vertical line represents the lowest temperature (power) at which equilibrium could be readily established in 100 minutes. All reported equilibrium data were collected at or above the highest threshold. It is important to note, however, that when evaluating the magnitude of any possible advantage of using microwaves to drive the steam-carbon reaction, it will be necessary to perform the reaction under kinetic conditions with flowing reactants. Under those conditions, parameters such as the power, flow rate, and carbon mass (i.e., path length) can be varied to optimize product production.

The equilibrium constants and associated thermochemical parameters that were determined for the steam-carbon process are important for understanding the magnitude and direction (exothermic or endothermic) of the microwave-specific effect. What is indicated by the enthalpy and entropy for the various constituent reactions of the process is that the microwave effect is quite pronounced, in most cases differing significantly from what is predicted for the conventional thermal reaction. However, the magnitude and direction of the apparent effects are reaction-dependent, with both increases and decreases in enthalpy and entropy observed.

We can obtain a useful measure of the magnitude and direction of the microwave-specific effect from thermodynamic consideration. The enthalpy of the gas-carbon reactions can be determined in the standard way from the standard enthalpies of the products and reactants at the reaction temperature, T, (equations 4-6). For the thermal reaction, this is the difference between the product and reactant, including the relevant stoichiometry factors (n).

$\begin{matrix} {{\Delta \; H_{thermal}} = {\left\lbrack {\sum\limits_{i}^{\;}\; {n_{i}\left( {\Delta \; H\; {^\circ}_{T}} \right)}} \right\rbrack_{product} - \left\lbrack {\sum\limits_{i}^{\;}{n_{i}\left( {\Delta \; H\; {^\circ}_{T}} \right)}} \right\rbrack_{reactants} - \left( {\Delta \; H\; {^\circ}_{T}} \right)_{C}}} & (4) \\ {{\Delta \; H_{microwave}} = {\left\lbrack {\sum\limits_{i}^{\;}\; {n_{i}\left( {\Delta \; H\; {^\circ}_{T}} \right)}} \right\rbrack_{product} - \left\lbrack {\sum\limits_{i}^{\;}{n_{i}\left( {\Delta \; H\; {^\circ}_{T}} \right)}} \right\rbrack_{reactants} - \left( {{\Delta \; H\; {^\circ}_{T}} + {\Delta \; H\; {^\circ}_{MW}}} \right)_{C}}} & (5) \\ {\mspace{79mu} {{{\Delta \; H_{thermal}} - {\Delta \; H_{microwave}}} = \left( {\Delta \; H\; {^\circ}_{MW}} \right)_{C}}} & (6) \end{matrix}$

For the gas phase reactants and products, it is assumed that even though the average temperature of the gas in the medium is much lower in the microwave experiment, the temperature of the gas equilibrates rapidly with the carbon surface when the reaction takes place. As such, the enthalpies are the same in both processes. We also assume, since carbon is the only reactant that directly absorbs the microwaves, that the magnitude of the microwave effect can be treated as a change in the apparent enthalpy of the carbon. We write the enthalpy as the sum of the thermal enthalpy and the enthalpy due to the microwave-specific contribution (eqn. 5). The magnitude of the microwave-specific enthalpy imparted to the carbon is simply the difference between the microwave and thermal reaction enthalpy (eqn. 6), which for the steam-carbon system is 129.0 kJ/mol. A similar analysis can be carried out for the entropy (ΔS_(ther)−ΔS_(mw)), which for the steam-carbon reaction is 128.6 J/mol. This value constitutes the apparent free entropy induced in the carbon by the microwave radiation. Clearly, from a thermodynamic standpoint, if the value obtained from equation 6 is positive, it appears as though extra heat (or entropy) is being “stored” in the carbon, whereas if it is negative, it appears as though there is an effective heat (or entropy) loss.

The key thermodynamic values for the thermal and microwave reactions and the magnitude and direction of the microwave-specific effect are summarized in Table 7. As discussed, for the steam-carbon and the Boudouard reaction, which are both strongly endothermic, the microwave effectively increases the enthalpy and entropy of the carbon, thereby making the overall reaction more exothermic and reducing the overall entropy.

TABLE 7 Thermodynamic Parameters for Thermal and Microwave Gas-Carbon Reactions thermal microwave ΔH ΔS ΔH ΔS microwave effect reaction (kJ/mol) (J/mol) (kJ/mol) (J/mol) (ΔH°)*_(C) (ΔS°)^(§) _(C) steam-carbon 144.2 158.1 15.2 29.5 129.0 128.6 Boudouard 180.2 191.2 27.0 43.1 153.2 148.1 WGS −36.0 −58.1 −11.4 −14.1 −24.6 −44.0 carbon- −79.7 −90.4 −9.1 −32.2 −70.6 −58.2 hydrogen *ΔH_(ther) − ΔH_(microwave); ^(§)ΔS_(ther) − ΔS_(microwave)

For the carbon-hydrogen reaction, which is inherently exothermic, the effect of the microwave is very different; it makes the reaction more endothermic and increases the effective entropy. The apparent effect on the carbon is that heat has been “removed” by the microwave.

Obviously, the microwave is not literally adding or subtracting heat (or entropy) to or from the carbon, respectively, due to its being held at certain temperatures that are the same for both the thermal and microwave reaction. The observed microwave effect on the thermodynamic properties of the reaction must be due to changes in the thermochemical kinetics of the forward and reverse reactions, which define the position of equilibrium. Since the gas phase species do not absorb microwaves, these thermodynamic changes must necessarily arise from changes in the reactivity of the carbon surface, or species adsorbed on the surface, through interactions with the radiation. In a simple fashion, the temperature dependence of the equilibrium constant and the forward and reverse rates can be written in terms of the free energy of activation.

$\begin{matrix} {K_{p} = {^{\frac{{- \Delta}\; G^{o}}{RT}} = {\frac{k_{1}}{k_{- 1}} = \frac{a_{1}^{\frac{- G_{1}^{*}}{RT}}}{a_{- 1}^{\frac{- G_{- 1}^{*}}{RT}}}}}} & (7) \\ {{\Delta \; G^{o}} = \left( {G_{1}^{*} - G_{- 1}^{*}} \right)} & (8) \end{matrix}$

In equation 7, the forward and reverse reactions have a free energy of activation associated with them and a pre-exponential factor, a, which will itself have a temperature dependence. See Houston, P. L. Chemical Kinetics and Reaction Dynamics, 1st ed.; Dover: Mineola, 2001. From this relationship, it can be seen that the free energy of the reaction is equal to the difference in the activation free energy of the forward and reverse reaction (eqn. 8). The effect of microwaves on the positions of the equilibrium can be interpreted as arising from differential changes in the forward and reverse activation parameters: free energy (G*) and selective heating (T, a). Since these are gas-solid reactions, the kinetics are not described by a pair of elementary opposing reactions but involve adsorption and desorption processes at the surface and reactions with active sites or other reactants on the carbon surface. As such, both the forward and reverse processes will have thermo-kinetic parameters associated with each discrete step in the mechanism, many of which can potentially be influenced by the microwave radiation.

In our prior study of the Boudouard reaction, we hypothesized that the enhanced reactivity and exothermic shift of the observed enthalpy under microwave conditions could potentially arise from interaction of the radiation with key mechanistic steps in the reaction. Specifically, we proposed that there were two places where microwave effects could manifest themselves. It is known that one of the primary dielectric loss processes, arising from the interaction of microwaves with carbon, is a space-charge mechanism (Maxwell-Wagner) where electron-hole pairs are generated and can be trapped at the surface. See Hotta, M.; Hayashi, M.; Lanagan, M. T.; Agrawal, D. K.; Nagata, K. Complex Permittivity of Graphite, Carbon Black and Coal Powders in the Ranges of X-band Frequencies (8.2 to 12.4 Ghz) and between 1 and 10 GHz. ISIJ Int. 2011, 51, 1766-1772; and Atwater, K. E.; Wheeler, R. R. Temperature Dependent Complex Permittivities of Graphitized Carbon Blacks at Microwave Frequencies between 0.2 and 26 GHz. J. Mater. Sci. 2004, 39, 151-157.

The electron-hole pairs are reactive and can potentially accelerate the oxidation of the surface by a substrate (CO₂ in the case of the Boudouard reaction). As we pointed out in our original study, the strength of this mechanism is that it is consistent with the known physics of microwave heating of carbon; however, given the difficulty of performing in situ analysis of the surface under microwave heating, it is difficult to prove, and other processes can certainly play a role.

Notably, a similar mechanism has been previously proposed to explain the influence of surface groups in the microwave-driven dry reforming of methane. See Fidalgo, B.; Arenillas, A.; Menendez, J. A. Influence of Porosity and Surface Groups on the Catalytic Activity of Carbon Materials for the Microwave-assisted CO₂ Reforming of CH₄ . Fuel 2010, 89, 4002-4007. In addition to activation of the surface, the microwaves can couple strongly with the dipole moments that form on the oxidized surface, thereby selectively heating them and accelerating the ejection of CO from the surface. The effectiveness of selective interfacial heating of surface-bound species has been well established in recent work by Conner. See Conner, W. C.; Tompsett, G. A. How Could and Do Microwaves Influence Chemistry at Interfaces? J. Phys. Chem. B 2008, 112, 2110-2118; Vallee, S. J.; Conner, W. C. Microwaves and Sorption on Oxides: A Surface Temperature Investigation. J. Phys. Chem. B 2006, 110, 15459-15470; and Vallee, S. J.; Conner, W. C. Effects of Microwaves and Microwave Frequency on the Selectivity of Sorption for Binary Mixtures on Oxides. J. Phys. Chem. C 2008, 112, 15483-15489.

Since the general mechanism of the steam-carbon and Boudouard reactions are believed to be essentially the same, the mechanism of microwave enhancement should also be similar. See Johnstone, H. F.; Chen, C. Y.; Scott, D. S. Kinetics of the Steam-Carbon Reaction in Porous Graphite Tubes. Ind. Eng. Chem. 1952, 44, 1564-1569; Long, F. J.; Sykes, K. W. The Catalysis of the Oxidation of Carbon. J. Chim. Phys.-Chim. Biol. 1950, 47, 361-378; Reif, A. E. The Mechanism of the Carbon Dioxide-Carbon Reaction. J. Phys. Chem. 1952, 56, 785-788. In particular, the first step is the oxidation of the carbon surface by H₂O or CO₂ for the steam-carbon and Boudouard reactions, respectively, which occurs with the concomitant elimination of H₂ and CO. The rate-determining step is the subsequent elimination of CO from the oxidized carbon surface. The reverse reaction will involve the H₂ or CO reacting with the oxidized surface to regenerate H₂O or CO₂.

Our hypothesis that the presence of electron-hole pairs creates a more easily oxidized carbon surface, thus reducing the free energy of activation of the forward oxidation process. This would tend to favor the forward reaction, consistent with the shift of the equilibrium to the right, under microwave irradiation. In the reactions considered here, the selective heating of the surface oxide by the microwave could result in both the acceleration of CO ejection from the oxidized surface which would enhance the forward reaction, or the enhancement of the reverse reaction, because the hot oxide groups react more readily with CO and H₂. In short, it could be argued that the microwaves can accelerate both the forward and reverse reactions. However, if the most facile process is CO dissociation from the surface (which is a unimolecular process), then the oxide groups will be rapidly depleted, thereby suppressing the reverse reaction.

For the WGS reaction, it is obvious that the selective microwave effect on the equilibrium constant arises from different magnitudes of microwave acceleration of the forward and reverse reaction. As discussed previously, the WGS reaction and its thermodynamic parameters are obtained simply from the difference between the steam-carbon (rxn. 1) and Boudouard reaction (rxn. 3). Mechanistically, the forward reaction involves initial oxidation of the carbon surface by water to produce hydrogen, with CO subsequently reacting with the oxidized surface to yield CO₂. As such, the observed microwave effect, in which the enthalpy of the reaction was found to be more endothermic, arises because the reverse reaction is simply the Boudouard reaction, which has a greater microwave-induced exothermicity (ΔH^(o) _(MW)) than does the forward, steam-carbon reaction, so the magnitude of the microwave effect of the WGS reaction in Table 7 is (ΔH^(o) _(MW))_(steam-carbon)−(ΔH^(o) _(MW))_(Boudouard)=−24.6 kJ/mol. An analogous analysis holds for the entropy.

For the carbon-hydrogen reaction (rxn. 4), the effect of the microwaves is to induce an endothermic shift in the thermodynamics, which shifts the equilibrium to the left, favoring the formation of H₂ from CH₄. This is potentially useful, as the reverse reaction will produce clean hydrogen fuel from hydrocarbons and, as such, is of significant interest. In fact, the reverse reaction is a key component of the dry reforming of methane (CH₄+CO₂→2CO+2H₂) over carbon, which has been found to be accelerated by microwaves. See Fidalgo, B.; Arenillas, A.; Menendez, J. A. Influence of Porosity and Surface Groups on the Catalytic Activity of Carbon Materials for the Microwave-assisted CO₂ Reforming of CH₄ . Fuel 2010, 89, 4002-4007; and Dominguez, A.; Fernandez, Y.; Fidalgo, B.; Pis, J. J.; Menendez, J. A. Biogas to Syngas by Microwave-assisted Dry Reforming in the Presence of Char. Energy Fuels 2007, 21, 2066-2071. The detailed mechanism of the carbon-hydrogen reaction has not been studied extensively, but the primary gas surface process for the forward reaction is thought to involve sequential hydrogenation of the carbon surface. For graphite, this takes place primarily at the edges of the basal plane. After a sufficient degree of hydrogenation, methane—the initial product—is eliminated. See Zielke, C. W.; Gorin, E. Kinetics of Carbon Gasification. Industrial and Engineering Chemistry 1957, 49, 396-403. The mechanism of the reverse reaction is not well understood and will depend on the nature of the carbon surface. It would involve dehydrogenation of the methane with the deposition of carbon on the surface followed and elimination of H₂. Whether this occurs in a concerted fashion or through the transfer of hydrogen to the carbon surface, from which it is subsequently eliminated.

The effect of microwaves on either of these reactions is difficult to assess. Using our model in which enhanced reactive sites are charge-separated sites on the surface induced by the microwave radiation, it is reasonable to suggest that the hydrogenation step, in both directions, might be accelerated, though possibly to different degrees. Alternatively, the acceleration of the reverse reactions may arise from the interfacial interactions of the C—H group with the microwave radiation, which may preferentially accelerate the elimination of H₂ from the surface in the reverse reaction over CH₄ in the forward reaction. Obviously, many other factors may be at play in such a mechanistically complex reaction.

When introducing elements of the present invention or the preferred embodiments(s) thereof, the articles “a”, “an”, “the” and “said” are intended to mean that there are one or more of the elements. The terms “comprising”, “including” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.

In view of the above, it will be seen that the several objects of the invention are achieved and other advantageous results attained.

As various changes could be made in the above products and methods without departing from the scope of the invention, it is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 

What is claimed is:
 1. A method of gasifying a source of carbon, the method comprising: irradiating the source of carbon with radiation having a frequency between 300 GHz and 300 MHz; and contacting the source of carbon with a reactant selected from the group consisting of water, carbon dioxide, hydrogen, a nitrogen oxide having formula NO_(x) wherein x has a value between 0.5 and 3, and any combination thereof; wherein said contact between the irradiated source of carbon and the reactant causes a reaction that yields a product selected from the group consisting of carbon monoxide, carbon dioxide, hydrogen, methane, nitrous oxide, nitric oxide, nitrogen, and any combination thereof.
 2. The method of claim 1 wherein the radiation has a frequency between about 1 GHz and about 18 GHz.
 3. The method of claim 1 wherein the radiation has a frequency between about 1 GHz and about 6 GHz.
 4. The method of claim 1 wherein the radiation has a frequency between about 1.5 GHz and about 3 GHz.
 5. The method of claim 1 wherein the radiation has a frequency between about 3 GHz and about 6 GHz.
 6. The method of claim 1 wherein the radiation has a frequency between about 6 GHz and about 10 GHz.
 7. The method of claim 1 wherein the radiation has a frequency between about 14 GHz and about 17 GHz.
 8. The method of claim 1 wherein the source of carbon and the reactant are additionally contacted with thermal heat.
 9. The method of claim 1 wherein the source of carbon comprises any carbon source capable of absorbing microwave radiation.
 10. The method of claim 1 wherein the source of carbon comprises any solid carbon source capable of absorbing microwave radiation.
 11. The method of claim 1 wherein the source of carbon is selected from the group consisting of amorphous carbon, charcoal, activated charcoal, carbon black, coal, graphite, coke, carbonized biomass, fullerene, carbon nanotubes, polyaromatic hydrocarbons, and any combination thereof.
 12. The method of claim 1 wherein the reactant comprises carbon dioxide, and the method yields a product comprising carbon monoxide.
 13. The method of claim 12, wherein the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 1:1 at a temperature less than 1000° C.
 14. The method of claim 12, wherein the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 2:1 at a temperature less than 920° C.
 15. The method of claim 12, wherein the composition of the gas at steady state conditions comprises a molar ratio of carbon monoxide (CO) to carbon dioxide (CO₂) of at least about 3:1 at a temperature less than 820° C.
 16. The method of claim 1 wherein the reactant comprises water, and the method yields a product comprising carbon monoxide and hydrogen.
 17. The method of claim 16 wherein the reactant comprises water, and the method yields a product comprising carbon monoxide, carbon dioxide, hydrogen, and methane.
 18. The method of claim 1 wherein the reactant comprises steam, and the method yields a product comprising carbon monoxide and hydrogen.
 19. The method of claim 18 wherein the reactant comprises steam, and the method yields a product comprising carbon monoxide, carbon dioxide, hydrogen, and methane.
 20. The method of claim 1 wherein the reactant comprises hydrogen, and the method yields a product comprising methane.
 21. The method of claim 1 wherein the reactant comprises the nitrogen oxide having formula NO_(x) wherein x has a value between 0.5 and
 3. 22. The method of claim 1 where in the nitrogen oxide is selected from the group consisting of NO₂, NO, N₂O, N₂O₂, N₂O₃, N₂O₄, N₂O₅, and any combination thereof. 